Sound Revision Notes

Sound is a form of energy that travels through a medium such as air, water, or solids as a wave. It is produced when an object vibrates, causing the particles in the surrounding medium to oscillate and transmit energy as sound waves. Without vibration, no sound is created.

• Sound requires a vibrating source.
• Vibrations cause particles in a medium to move.
• Sound travels as waves through a medium.

When an object vibrates, it moves rapidly back and forth from its rest position. This movement pushes nearby particles in the medium closer together (compression) and then pulls them apart (rarefaction). These alternating compressions and rarefactions form longitudinal sound waves that travel through the medium.

The particles themselves do not travel with the wave; instead, they oscillate about fixed positions, transferring energy from one particle to the next.

• Vibrations cause compressions and rarefactions in the medium.
• Sound waves are longitudinal waves consisting of pressure variations.
• Particles oscillate parallel to the direction of wave travel.

The frequency of the vibrations of the source determines the frequency of the sound wave produced. Frequency is the number of vibrations per second and is measured in hertz (Hz).

A higher frequency vibration produces a higher pitch sound, while a lower frequency vibration produces a lower pitch sound. For example, a guitar string vibrating faster produces a higher note than one vibrating slower.

• Frequency (Hz) = number of vibrations per second.
• Higher frequency → higher pitch.
• Lower frequency → lower pitch.

The amplitude of the vibration is related to the maximum displacement of the vibrating object from its rest position. Larger amplitude vibrations cause greater pressure variations in the medium, producing sound waves with higher amplitude.

The amplitude of the sound wave determines the loudness of the sound. Greater amplitude means a louder sound, while smaller amplitude means a quieter sound.

• Amplitude is the maximum displacement of vibration.
• Greater amplitude → louder sound.
• Smaller amplitude → quieter sound.

To draw a diagram illustrating sound production by a vibrating object:

1. Draw a horizontal line representing the rest position of the object.

2. Sketch the object displaced to the right and left of the rest position to show vibration (back and forth motion). Label these as 'Vibration'.

• Show compressions as regions where particles are close together.
• Show rarefactions as regions where particles are spread apart.
• Label the wave as a longitudinal sound wave propagating through the medium.

Sound waves are mechanical waves that require a material medium (solid, liquid, or gas) to travel through. They cannot propagate through a vacuum because they rely on particle interactions within the medium.

Unlike transverse waves, where particle vibration is perpendicular to wave direction, sound waves are longitudinal. This means the particles vibrate back and forth in the same direction as the wave travels.

The vibration of particles causes alternating regions of high and low pressure in the medium, known as compressions and rarefactions respectively.

• Sound waves need a medium to travel.
• They are longitudinal waves.
• Particles vibrate parallel to wave direction.
• Compressions are regions of high pressure.
• Rarefactions are regions of low pressure.

In a longitudinal wave, particles oscillate about their equilibrium positions along the direction of energy transfer. For sound, this means particles move forward and backward along the path the wave travels.

As a sound wave passes, particles are pushed closer together forming compressions, then pulled apart forming rarefactions. These alternating compressions and rarefactions move through the medium, transferring energy without net particle displacement.

This particle motion can be visualised by imagining a slinky stretched out horizontally. If you push and pull one end along its length, compressions and expansions travel along the slinky, similar to sound waves in air.

• Particles oscillate parallel to wave travel direction.
• Compressions: particles close together, high pressure.
• Rarefactions: particles spread apart, low pressure.
• Energy transfer occurs without net particle movement.
• Slinky analogy illustrates longitudinal wave motion.

Compressions are regions where particles are densely packed, resulting in higher pressure and density than the surrounding medium.

Rarefactions are regions where particles are spread out, resulting in lower pressure and density.

The wavelength of a sound wave is the distance between two successive compressions or two successive rarefactions, measured in metres (m). The frequency (Hz) and speed (m/s) of sound relate to wavelength by the equation: v = f × λ, where v is wave speed, f is frequency, and λ is wavelength.

• Compression: high pressure, particles close.
• Rarefaction: low pressure, particles apart.
• Wavelength is distance between compressions or rarefactions.
• Wave speed equation: v = f × λ.

Sound waves are mechanical waves; they transfer energy via particle vibrations. Without particles to vibrate, such as in a vacuum, sound cannot propagate.

The medium's particles interact through collisions and elastic forces, allowing the wave to move through the medium.

The speed of sound depends on the medium's properties: it travels fastest in solids (particles closely packed), slower in liquids, and slowest in gases due to particle spacing and elasticity.

• Sound needs particles to vibrate; no sound in vacuum.
• Medium particles transmit energy via collisions.
• Speed depends on medium density and elasticity.
• Fastest in solids, slower in liquids, slowest in gases.

To draw a longitudinal wave representing sound: start with a horizontal baseline representing the undisturbed medium.

Draw regions where particles are close together (compressions) as vertical lines or shaded areas.

Draw regions where particles are spread apart (rarefactions) as wider spaces between lines or unshaded areas between compressions, alternating along the baseline direction from left to right to show wave propagation direction.

• Baseline represents undisturbed medium.
• Compressions shown as closely spaced lines or shaded regions.
• Rarefactions shown as widely spaced lines or gaps.
• Wave propagates left to right along baseline.
• Particle vibration direction is parallel to wave direction.

Sound is a mechanical wave that travels through a medium such as air, water, or solids. It is characterised by its frequency, which is the number of vibrations or oscillations per second, measured in hertz (Hz).

The frequency of a sound wave determines its pitch: low frequencies produce low-pitched sounds (bass), and high frequencies produce high-pitched sounds (treble).

• Frequency (f) is measured in hertz (Hz).
• Pitch is the human perception of frequency.
• Low frequency = low pitch; high frequency = high pitch.

The human ear can detect sounds with frequencies approximately between 20 Hz and 20,000 Hz (20 kHz). This range is called the audible range.

Sounds below 20 Hz are called infrasound and are generally inaudible to humans, while sounds above 20 kHz are called ultrasound and are also inaudible to humans.

The audible range varies slightly between individuals and tends to decrease with age, especially at the high-frequency end.

• Audible frequency range: 20 Hz to 20,000 Hz.
• Infrasound: frequencies below 20 Hz (inaudible).
• Ultrasound: frequencies above 20,000 Hz (inaudible).
• Age and hearing health affect audible range.

The ear detects sound waves through vibrations of the eardrum and inner ear structures, which respond to specific frequency ranges.

At very low frequencies (below 20 Hz), the ear cannot detect the vibrations as sound but may sense them as vibrations.

At very high frequencies (above 20 kHz), the ear's sensory cells do not respond effectively, so these sounds are not perceived.

• Eardrum and cochlea respond to 20 Hz–20 kHz.
• Below 20 Hz: vibrations felt, not heard.
• Above 20 kHz: sensory cells do not respond.

The audible frequency range covers most sounds important for human communication, including speech and music.

Musical instruments produce sounds within this range, allowing humans to perceive melody and harmony.

Understanding this range is important in designing audio equipment, hearing aids, and soundproofing materials.

• Speech frequencies mostly between 300 Hz and 3,400 Hz.
• Music spans from about 20 Hz to 20 kHz.
• Audio devices are designed for this range.

To draw a frequency range diagram: Draw a horizontal line labelled 'Frequency (Hz)' with values from 0 to 25,000 Hz marked at regular intervals.

Mark the audible range from 20 Hz to 20,000 Hz with a coloured bar or bracket labelled 'Human audible range'.

Label frequencies below 20 Hz as 'Infrasound' and above 20,000 Hz as 'Ultrasound'.

• X-axis: Frequency (Hz) from 0 to 25,000 Hz.
• Highlight 20 Hz to 20,000 Hz as audible range.
• Label regions outside audible range accordingly.

Sound waves are longitudinal mechanical waves produced by vibrating objects. These vibrations cause particles in the surrounding medium to oscillate parallel to the direction of wave travel, creating regions of compression and rarefaction.

Because sound waves involve the oscillation of particles, they require a medium composed of matter—such as air, water, or solids—to carry the wave energy from one place to another.

Unlike electromagnetic waves, sound waves cannot propagate through empty space (a vacuum) because there are no particles to vibrate and transmit the wave.

• Sound waves are longitudinal mechanical waves.
• They consist of compressions and rarefactions in the medium.
• They require particles in a medium to transfer energy.

Sound can travel through all three states of matter: gases, liquids, and solids. The particles in these media vibrate and pass on the sound energy to neighbouring particles.

In gases (e.g., air), particles are far apart, so sound travels slower compared to liquids and solids where particles are closer together.

The medium’s density and elasticity affect the speed and quality of sound transmission.

• Sound travels through gases, liquids, and solids.
• Particle spacing and bonding affect sound speed.
• Sound speed is generally fastest in solids, slower in liquids, and slowest in gases.

A vacuum is a space devoid of matter, meaning it contains no particles to vibrate and transmit sound waves.

Since sound waves depend on particle vibrations to propagate, the absence of particles in a vacuum prevents sound from travelling.

This is why sound cannot be heard in outer space or in evacuated containers.

• Vacuum contains no particles.
• No medium means no transmission of sound.
• Sound cannot travel through a vacuum.

The speed of sound depends on the medium’s density and elasticity. More elastic and less dense media allow faster sound propagation.

For example, sound travels approximately 330–350 m/s in air at room temperature, about 1500 m/s in water, and up to 5000 m/s in steel.

Temperature and pressure can also affect sound speed in gases by changing particle energy and spacing.

• Sound speed varies with medium properties.
• Sound travels fastest in solids, slower in liquids, slowest in gases.
• Temperature affects sound speed in gases.

The speed of sound in air is the distance travelled by a sound wave per unit time as it moves through the air. It is a scalar quantity measured in metres per second (m/s). Under normal atmospheric conditions (around 20°C and at sea level), the speed of sound in air is approximately between 330 m/s and 350 m/s.

This means that a sound wave travels roughly 330 to 350 metres every second through air at room temperature. This value is an average because the speed of sound depends on the properties of the air through which it travels.

• Speed of sound in air ≈ 330 to 350 m/s at 20°C.
• Unit of speed: metres per second (m/s).

The speed of sound in air is not constant and varies mainly with temperature and humidity. Sound waves travel by vibrating air particles; warmer air causes particles to move faster, allowing sound waves to propagate more quickly.

Humidity also affects sound speed because moist air contains water vapour, which is less dense than dry air. This reduces the overall density of the air, increasing the speed of sound.

Pressure changes at constant temperature have little effect on sound speed because both air density and elasticity change proportionally, cancelling out their effects on speed.

• Higher temperature increases speed of sound.
• Greater humidity increases speed of sound.
• Pressure changes have negligible effect at constant temperature.

Sound is a mechanical longitudinal wave that travels by compressions and rarefactions of air molecules. The speed of sound depends on the medium's elasticity and density. In air, elasticity is related to how easily air molecules return to their original position after being disturbed, and density is the mass per unit volume.

Warmer air has molecules moving faster and spaced further apart, reducing density and increasing elasticity, which raises sound speed. Similarly, humid air has lighter water molecules replacing heavier nitrogen and oxygen molecules, lowering density and increasing speed.

• Speed depends on medium's elasticity and density.
• Warmer air increases elasticity and decreases density.
• Humid air decreases density, increasing speed.

If a sound wave travels 340 metres in one second, its speed is 340 m/s. The formula for speed is:

\[ \text{speed} = \frac{\text{distance}}{\text{time}} \]

For example, if a sound wave travels 680 metres in 2 seconds: \[ \text{speed} = \frac{680\,\text{m}}{2\,\text{s}} = 340\,\text{m/s} \]

• Speed = distance ÷ time.
• Units: metres (m) for distance, seconds (s) for time, speed in m/s.
• Example: 680 m in 2 s → speed = 340 m/s.

In practical experiments to measure the speed of sound, students measure the time taken for a sound to travel a known distance. Repeating measurements and averaging results improves accuracy. Temperature should be recorded because it affects the speed. Safety precautions include avoiding loud noises that could damage hearing.

To improve accuracy, use longer distances to reduce timing errors and use precise timing devices such as electronic timers or microphones connected to oscilloscopes.

• Measure distance and time accurately.
• Repeat measurements and calculate average.
• Record air temperature for reference.
• Avoid loud noises to protect hearing.

Sound is a mechanical wave that travels through air at a certain speed, typically around 330 to 350 m/s at room temperature. Measuring this speed experimentally involves determining how long it takes for sound to travel a known distance. The speed of sound (v) is calculated using the formula:

\n\nv = \frac{d}{t} \n\nwhere v is speed in metres per second (m/s), d is distance in metres (m), and t is time in seconds (s).

• Speed of sound depends on the medium and conditions such as temperature.
• Measuring time and distance accurately is essential for a reliable result.

To measure the speed of sound in air, you need: a stopwatch or timer with at least 0.1 s resolution, two markers placed a known distance apart (for example, 100 m), and a method to produce a sharp, loud sound (such as clapping hands or a starter pistol).

One person stands at the first marker (point A) and another at the second marker (point B). The distance between the markers must be measured precisely using a tape measure or trundle wheel.

• Stopwatch or digital timer.
• Two markers placed a known distance apart (e.g., 100 m).
• Sound source (clap, whistle, starter pistol).
• Measuring tape or trundle wheel for distance.

1. Measure and record the distance (d) between the two markers accurately.

2. The person at point A produces a sharp sound (e.g., clap).

3. The person at point B watches the person at point A and starts the stopwatch the instant they see the sound being made (visual cue). This avoids reaction delay in starting the timer after hearing the sound, which would cause error. Alternatively, the person at point B can start the stopwatch on seeing the signal and stop it when they hear the sound arrive, measuring the time taken for sound to travel from A to B.

• Start timing when the sound is produced (using visual cue).
• Stop timing when the sound is heard at the second marker.
• Record the time interval (t).
• Repeat several times for accuracy and calculate the average time.

Use the formula: speed = distance ÷ time, or mathematically:

\n\nv = \frac{d}{t} \n\nwhere: d = distance between markers in metres (m), t = time taken for sound to travel this distance in seconds (s), v = speed of sound in metres per second (m/s).

Example: If the distance is 100 m and the average time measured is 0.29 s, then: \n\nv = \frac{100\,\text{m}}{0.29\,\text{s}} = 344.8\,\text{m/s} \approx 345\,\text{m/s} \n\nThis value is consistent with typical speed of sound in air at room temperature.

• Always include units in calculations.
• Repeat measurements to reduce random errors.
• Calculate average time before computing speed.

Several factors affect the accuracy of this measurement:

Reaction time: Human reaction delays in starting/stopping the stopwatch can cause errors. Using a visual cue to start timing helps reduce this.

Environmental conditions: Temperature, humidity, and wind affect sound speed. Warmer air increases speed; cold air decreases it. Record ambient temperature if possible to compare with expected values.

• Repeat the experiment multiple times and average results to reduce random errors.
• Use longer distances to reduce relative timing errors.
• Minimise background noise to clearly hear the sound.
• Ensure the line between markers is straight and unobstructed.
• Consider environmental factors (temperature, humidity).

Sound is a mechanical wave that travels through a medium by vibrating particles. It is a longitudinal wave characterised by compressions and rarefactions.

Two fundamental properties of sound waves are amplitude and frequency. Amplitude is the maximum displacement of particles from their rest position in the wave, measured in metres (m). Frequency is the number of complete vibrations or cycles per second, measured in hertz (Hz).

Amplitude and frequency determine how we perceive sound in terms of loudness and pitch, respectively.

• Amplitude: maximum particle displacement (m)
• Frequency: cycles per second (Hz)
• Sound waves are longitudinal waves with compressions and rarefactions

Loudness is the subjective perception of the intensity of a sound. It depends primarily on the amplitude of the sound wave.

A larger amplitude means the particles in the medium vibrate with greater displacement, transferring more energy per second to the ear. This results in a louder sound.

Amplitude is proportional to the energy carried by the wave and thus to loudness. Doubling the amplitude increases the loudness significantly, but loudness perception is not linear; it depends on the logarithmic response of the ear (measured in decibels, dB).

• Loudness increases with amplitude
• Amplitude relates to energy transferred by the wave
• Loudness is measured in decibels (dB), a logarithmic scale

Pitch is the subjective perception of how high or low a sound is. It depends on the frequency of the sound wave.

Higher frequency means more vibrations per second, which the brain interprets as a higher pitch.

Humans typically hear frequencies from about 20 Hz (low pitch) to 20,000 Hz (high pitch). Sounds above 20,000 Hz are ultrasound and below 20 Hz are infrasound, both inaudible to humans.

• Pitch increases with frequency
• Frequency measured in hertz (Hz)
• Human hearing range: approximately 20 Hz to 20,000 Hz

Amplitude corresponds to the height of the wave crest or depth of the trough in a displacement-time or displacement-distance graph of a sound wave.

Frequency corresponds to how many complete waves pass a point per second, inversely related to the wavelength (λ) by the wave speed equation: v = f × λ, where v is speed (m/s), f is frequency (Hz), and λ is wavelength (m).

Increasing amplitude increases the wave's energy but does not affect frequency or wavelength. Increasing frequency raises pitch but does not affect amplitude or loudness directly.

• Amplitude = wave height on graph
• Frequency = number of waves per second
• Wave speed equation: v = f × λ

Musical instruments produce sounds by vibrating objects; changing the amplitude of vibration changes loudness, while changing the frequency changes pitch.

Electronic sound devices can alter amplitude and frequency independently to produce desired loudness and pitch.

In sound engineering, amplitude is controlled by volume settings, and frequency by tuning or equalisation. Understanding these relationships is essential for sound design and acoustics.

• Amplitude controls loudness in instruments and devices
• Frequency controls pitch in instruments and devices
• Applications include music, speech, and audio technology

An echo is the sound heard after the original sound wave is reflected from a surface and returns to the listener. It occurs when sound waves travel through a medium, such as air, hit a hard, smooth surface, and bounce back. The reflected sound wave must reach the listener with a sufficient time delay to be perceived as a distinct repetition of the original sound rather than a continuation.

• Echo is a reflected sound wave.
• It must be heard after a noticeable delay from the original sound.
• Reflection occurs at surfaces that are hard and smooth.

Sound waves are longitudinal waves that travel through a medium by compressions and rarefactions. When these waves encounter a surface, part of the wave energy is reflected back. The angle of incidence equals the angle of reflection, similar to light waves, but this is less commonly measured for sound. The quality of the reflecting surface affects the strength and clarity of the echo.

• Sound waves reflect off surfaces, producing echoes.
• Hard, smooth surfaces reflect sound better than soft or irregular surfaces.
• The reflected wave travels back to the source or listener.

To hear an echo, the reflected sound must arrive at the listener's ear at least 0.1 seconds after the original sound. This delay allows the brain to distinguish the echo from the initial sound. Since the speed of sound in air is approximately 340 m/s, the reflecting surface must be at least 17 metres away (because the sound travels to the surface and back, total distance is 2 × 17 m = 34 m, and time = distance/speed = 34/340 = 0.1 s).

• Minimum time delay for an echo to be heard is about 0.1 seconds.
• Reflecting surface must be at least 17 metres away.
• Speed of sound in air is approximately 340 m/s.

Echoes can be used to measure the distance to a reflecting surface by timing how long it takes for the sound to travel to the surface and back. The formula used is: distance = (speed of sound × time) ÷ 2. The division by 2 accounts for the sound travelling to the surface and returning. For example, if the time between the original sound and the echo is 0.5 seconds, the distance to the surface is (340 m/s × 0.5 s) ÷ 2 = 85 metres.

• Distance = (speed of sound × time) ÷ 2.
• Time is the total travel time for the sound to go and return.
• Used in sonar and other distance-measuring technologies.

Echoes are used in sonar systems to detect objects underwater by sending sound pulses and measuring the time for echoes to return. They are also used in architectural acoustics to design auditoriums and concert halls to control sound reflections. Understanding echoes helps in reducing unwanted noise and improving sound clarity.

• Sonar uses echoes to detect underwater objects.
• Architectural design uses echo control for better acoustics.
• Echoes help in distance measurement and object detection.

Sound waves are mechanical longitudinal waves that travel through a medium by particle vibrations. The frequency of a sound wave is the number of vibrations or cycles per second, measured in hertz (Hz).

Humans can typically hear sounds with frequencies from about 20 Hz to 20,000 Hz (20 kHz). Frequencies below 20 Hz are called infrasound, and frequencies above 20 kHz are called ultrasound.

The audible range varies slightly between individuals and decreases with age, especially at higher frequencies.

• Frequency (f) is measured in hertz (Hz).
• Human audible range: approximately 20 Hz to 20 kHz.
• Sounds above 20 kHz are inaudible to humans.

Ultrasound is defined as sound waves with frequencies greater than 20 kHz (20,000 Hz).

Because these frequencies are above the human hearing range, ultrasound waves cannot be heard by people.

Ultrasound waves have shorter wavelengths than audible sound waves, which allows them to interact with small structures and boundaries in materials.

• Ultrasound frequency: f > 20 kHz.
• Ultrasound waves are inaudible to humans.
• Shorter wavelength than audible sound waves.

Ultrasound waves are longitudinal waves, consisting of compressions and rarefactions in the medium.

The wavelength (λ) of ultrasound is related to its frequency (f) and the speed of sound (v) in the medium by the equation: λ = v / f.

Because ultrasound frequencies are high, their wavelengths are very short, enabling high-resolution imaging and precise detection of small features in materials.

• Ultrasound waves are longitudinal.
• Wavelength λ = v / f, where v is speed of sound in the medium.
• Short wavelengths enable detailed imaging and detection.

Ultrasound is widely used in medical imaging, such as scanning internal organs and monitoring foetal development, due to its ability to produce detailed images without ionising radiation.

It is also used in industrial non-destructive testing to detect flaws in materials and in cleaning delicate objects by ultrasonic agitation.

These applications exploit the high frequency and short wavelength of ultrasound waves.

• Medical imaging (e.g., foetal scans).
• Industrial non-destructive testing.
• Ultrasonic cleaning.

Sound waves are longitudinal mechanical waves that require a medium (solid, liquid, or gas) to travel. Unlike transverse waves, the oscillations of particles in the medium are parallel to the direction of wave propagation.

As a sound wave travels, it causes particles in the medium to vibrate back and forth along the same line as the wave moves. These vibrations create regions where particles are alternately pushed together and pulled apart.

• Sound waves are longitudinal waves.
• Particles oscillate parallel to wave direction.
• Require a medium to propagate.

Compression is a region in a sound wave where particles of the medium are pushed closer together than their normal equilibrium spacing. This results in an increase in local pressure and density.

During compression, the air pressure is higher than the atmospheric pressure. The particles are crowded, causing a temporary increase in pressure that moves through the medium as the wave travels.

Compression corresponds to the peak of the pressure wave in the sound wave cycle.

• Compression = particles close together.
• Pressure and density increase in compression.
• Compression moves through the medium as a high-pressure region.

Rarefaction is the opposite of compression. It is a region where particles are spread further apart than their normal spacing, causing a decrease in local pressure and density.

In rarefaction, the air pressure is lower than atmospheric pressure. The particles are more spaced out, creating a low-pressure region that travels through the medium.

Rarefaction corresponds to the trough of the pressure wave in the sound wave cycle.

• Rarefaction = particles spread apart.
• Pressure and density decrease in rarefaction.
• Rarefaction moves through the medium as a low-pressure region.

Sound propagates as a series of alternating compressions and rarefactions moving through the medium. Each particle oscillates about its equilibrium position, transferring energy to neighbouring particles.

The wave consists of these pressure variations travelling through the medium at the speed of sound, which depends on the medium's properties.

The wavelength is the distance between two successive compressions or two successive rarefactions. The frequency is the number of compressions (or rarefactions) passing a point per second.

• Sound wave = alternating compressions and rarefactions.
• Particles oscillate about equilibrium, transferring energy.
• Wavelength = distance between compressions or rarefactions.
• Frequency = number of compressions passing per second.

A longitudinal wave diagram can be drawn as a horizontal line representing the medium at rest. Along this line, draw regions where particles are close together (compressions) and regions where particles are spread apart (rarefactions).

Label compressions as regions of high pressure and rarefactions as regions of low pressure.

This diagram helps visualise how sound waves propagate through the medium by alternating pressure changes.

• Draw a horizontal baseline for equilibrium particle positions.
• Mark compressions as closely spaced particles (high pressure).
• Mark rarefactions as widely spaced particles (low pressure).
• Label compressions and rarefactions accordingly.

Sound is a mechanical wave produced by vibrating objects. It requires a medium—solid, liquid, or gas—to travel because it propagates through the vibration of particles in the medium.

The particles in the medium oscillate about their equilibrium positions, transferring energy from one particle to the next. This transfer of energy constitutes the sound wave moving through the medium.

Sound waves are longitudinal waves, meaning the particle vibrations are parallel to the direction of wave travel.

• Sound requires a medium to travel; it cannot travel through a vacuum.
• Sound waves involve particle vibrations transmitting energy through the medium.

The speed of sound in a medium depends primarily on two physical properties: the medium's elasticity and its density.

Elasticity is the ability of the medium to return to its original shape after being disturbed. A more elastic medium transmits sound faster because particles can quickly restore their positions, facilitating rapid energy transfer.

Density is the mass per unit volume of the medium. A denser medium has more mass for the sound wave to move, which tends to slow down the wave's speed.

• Higher elasticity increases sound speed.
• Higher density tends to decrease sound speed.
• The combined effect of elasticity and density determines the actual speed of sound in a medium.

In solids, particles are tightly packed and strongly bonded, giving solids high elasticity and relatively high density. The strong bonds allow particles to quickly transmit vibrations, resulting in the fastest speed of sound among the three states of matter.

In liquids, particles are less tightly packed than in solids and have weaker bonds, so elasticity is lower. Density is generally less than solids but more than gases. Sound travels slower in liquids than in solids but faster than in gases.

In gases, particles are far apart with weak interactions, resulting in low elasticity and low density. The large distances between particles mean sound waves take longer to transfer energy, so sound travels slowest in gases.

• Sound speed order: solids > liquids > gases.
• Typical speed in air (gas) is about 330–350 m/s.
• Typical speed in water (liquid) is about 1480 m/s.
• Typical speed in steel (solid) is about 5000 m/s.

The speed of sound varies with the medium and conditions such as temperature, but typical values at room temperature are:

Air (gas): approximately 340 m/s, depending on temperature and humidity.

Water (liquid): approximately 1480 m/s, much faster than in air due to higher elasticity and density balance in water compared to air. Steel (solid): approximately 5000 m/s, due to very high elasticity and particle density.

• Speed of sound in air ≈ 340 m/s.
• Speed of sound in water ≈ 1480 m/s.
• Speed of sound in steel ≈ 5000 m/s.

Because sound travels fastest in solids, it is possible to hear sounds transmitted through solid materials before hearing them through air. This principle is used in applications such as seismic surveys and structural health monitoring.

Understanding the speed of sound in different media is essential for technologies like sonar, ultrasound imaging, and acoustic engineering.

When solving problems involving sound speed, always identify the medium and use the appropriate speed value or formula.

• Sound speed depends on medium's elasticity and density.
• Sound travels fastest in solids, slower in liquids, slowest in gases.
• Applications rely on knowledge of sound speed in various media.

When a sound pulse is emitted towards an object, it travels through a medium (such as air or water), reflects off the object, and returns to the source as an echo or reflected pulse.

The total time measured, t, is the time taken for the pulse to travel from the source to the object and back again.

Since the pulse travels the distance twice (to the object and back), the one-way distance d to the object is half the total distance travelled by the pulse.

• Pulse travels to object and reflects back.
• Total travel time includes both outward and return journeys.
• One-way distance is half the total distance travelled.

The speed of sound in the medium is v (in metres per second, m/s).

The total time for the pulse to travel to the object and back is t (in seconds, s).

The total distance travelled by the pulse is vt (speed × time). Since this includes the journey to the object and back, the one-way distance d is: d = vt / 2.

• d = vt / 2 where:
• d = one-way distance (m)
• v = speed of sound in the medium (m/s)
• t = total time for pulse to travel to object and back (s)

A sonar device emits an ultrasound pulse towards the seabed. The reflected pulse returns after 0.50 seconds. The speed of sound in water is approximately 1500 m/s.

Calculate the depth of the seabed (one-way distance).

• Given: t = 0.50 s, v = 1500 m/s
• Use formula: d = vt / 2
• Substitute values: d = (1500 m/s × 0.50 s) / 2 = 750 / 2 = 375 m
• Answer: The seabed is 375 metres deep.

A frequent mistake is to use d = vt directly, which gives the total distance travelled by the pulse (to the object and back), not the one-way distance.

Always remember that the measured time t includes the pulse travelling twice the one-way distance.

Ensure units are consistent: speed in m/s, time in seconds, distance in metres.

• Do not omit dividing by 2 in the formula.
• Check units carefully before substituting.
• Interpret the time t as total travel time, not one-way time.

Ultrasound or sonar devices use this principle to measure distances underwater or in solids where light cannot penetrate.

The accuracy depends on precise measurement of the time interval t and knowing the correct speed of sound in the medium.

Temperature, pressure, and medium composition affect the speed of sound and should be considered for precise measurements.

• Use accurate timing devices to measure t.
• Use correct value of v for the medium and conditions.
• Repeat measurements to improve reliability.
• Be aware of environmental factors affecting sound speed.