Waves in matter Revision Notes

What is Wavelength?

Wavelength is defined as the distance between two consecutive corresponding points on a wave. This could be from one crest to the next crest, or from one trough to the next trough. It represents one complete cycle of the wave. The standard symbol for wavelength is the Greek letter lambda (λ), and it is typically measured in metres (m). Wavelength helps describe the spatial extent of a wave.

What is Frequency?

Frequency is defined as the number of complete waves or cycles that pass a fixed point in one second. It tells us how often a wave oscillates. The standard symbol for frequency is 'f', and its unit is the Hertz (Hz). One Hertz is equivalent to one cycle per second (s⁻¹). A higher frequency means more waves are passing by per unit time.

Relationship between Wavelength and Frequency

Wavelength and frequency are inversely proportional for a wave traveling at a constant speed. This means that as the wavelength of a wave increases, its frequency decreases, and vice versa. For example, waves with short wavelengths have high frequencies, while waves with long wavelengths have low frequencies. This fundamental relationship is expressed by the wave equation: wave speed (v) = frequency (f) × wavelength (λ). Understanding this relationship is key to comprehending wave behaviour.

Understanding Ionising Radiation

Ultraviolet (UV) waves, X-rays, and gamma rays are all forms of ionising radiation. This means they carry enough energy to remove electrons from atoms, creating ions. This process, called ionisation, can disrupt the normal chemical structure of biological molecules within cells, including DNA. Damage to DNA can lead to uncontrolled cell growth (cancer), cell malfunction, or cell death. The more energy these waves impart, the greater the potential for biological damage.

Hazards of Ultraviolet (UV) Radiation

UV radiation is primarily associated with sunlight exposure. Its effects are mainly on surface tissues like the skin and eyes. Short-term effects include sunburn and blistering. Long-term exposure to UV radiation significantly increases the risk of premature skin ageing, skin cancer (such as melanoma), and damage to the eyes, which can lead to cataracts. Protection includes sunscreen, protective clothing, and sunglasses.

Hazards of X-rays and Gamma Rays

X-rays and gamma rays are much more penetrating than UV radiation and can deeply affect internal bodily tissues and organs. Exposure to high doses can cause acute radiation sickness, presenting symptoms like nausea, vomiting, diarrhoea, hair loss, and a weakened immune system. Significantly, these radiations can damage bone marrow, leading to anaemia and increased susceptibility to infection. Long-term exposure or high doses increase the risk of various cancers (e.g., leukaemia, thyroid cancer), genetic mutations, and birth defects in offspring if reproductive cells are affected. Medical uses of X-rays are carefully controlled to minimise patient exposure.

Factors Influencing Harm and Safety Precautions

The extent of harm from UV, X-rays, and gamma rays depends on the type of radiation, the energy delivered (dose), the duration of exposure, and the specific tissues or organs exposed. More sensitive tissues, like bone marrow or reproductive organs, are particularly vulnerable. Safety precautions include using shielding materials (e.g., lead for X-rays/gamma rays), limiting exposure time, increasing distance from the source, and using protective eyewear and clothing. Regular monitoring using dosimeters is crucial for professionals working with these radiations.

The Mechanism of Sound-to-Vibration Conversion

Sound waves are longitudinal waves characterized by compressions (regions of higher pressure/density) and rarefactions (regions of lower pressure/density) in a medium. When a sound wave encounters a solid boundary, the varying pressure of the sound wave exerts a force on the surface of the solid. This force causes the particles of the solid to oscillate or vibrate at the same frequency as the incoming sound wave. The amplitude of these solid vibrations depends on the intensity of the sound wave and the physical properties of the solid, such as its mass, stiffness, and damping characteristics. A classic example is a microphone diaphragm, which is a thin, flexible solid. As sound waves strike it, the diaphragm is pushed and pulled, converting the acoustic energy into mechanical vibrations.

The Mechanism of Vibration-to-Sound Conversion

Conversely, a vibrating solid can act as a source of sound waves. When a solid object vibrates, its surface moves back and forth. As it moves forward, it compresses the air or other surrounding medium in front of it, increasing the pressure. As it moves backward, it creates a region of lower pressure, or a rarefaction. These alternating compressions and rarefactions propagate outwards from the vibrating surface as a sound wave. The frequency of the emitted sound wave is identical to the frequency of the solid's vibration. The amplitude of the sound wave depends on the amplitude of the solid's vibration and the solid's surface area that is in contact with the medium. A loudspeaker cone is a prime example; its vibrations are driven by electrical signals, and these mechanical movements push and pull the air, creating the sound we hear.

Examples in Acoustic Devices (Higher)

Many everyday devices rely on the conversion between sound waves and solid vibrations. Microphones convert sound into electrical signals via mechanical vibrations of a diaphragm. In a dynamic microphone, sound waves cause a diaphragm to vibrate, moving a coil within a magnetic field to generate an electrical current. Loudspeakers convert electrical signals back into sound; an electrical current causes a coil and attached cone to vibrate, pushing air to create sound waves. Musical instruments also demonstrate this: the vibration of strings (e.g., guitar, piano), membranes (e.g., drum), or air columns (e.g., flute) generates sound waves which then propagate through the air. The eardrum in the human ear is another prime biological example, vibrating in response to sound waves and transmitting these vibrations to ossicles.

Factors Affecting Conversion (Higher)

The efficiency and characteristics of the conversion process are influenced by several factors. Material properties are critical; for instance, a highly compliant (flexible) material will vibrate more readily than a very stiff one when subjected to sound waves of the same intensity. The mass of the vibrating object also plays a role, with lighter objects generally responding more readily to high-frequency sounds. The coupling between the solid and the surrounding medium is also important. Good acoustic coupling, such as a large surface area in contact with the air, enhances sound radiation from a vibrating solid. Resonance is a key phenomenon where if the frequency of the incoming sound matches the natural frequency of vibration of the solid, the amplitude of the solid's vibration can significantly increase, leading to a much more efficient energy transfer.

The Wave Equation and Sound

Sound waves, like all waves, obey the wave equation: velocity (v) = frequency (f) × wavelength (λ). This equation shows how the speed of a wave is determined by its frequency and its wavelength. For sound, velocity depends on the medium it is travelling through. Sound travels fastest in solids, then liquids, and slowest in gases because of the differing particle arrangements and how easily vibrations can be transmitted. Frequency is measured in Hertz (Hz), wavelength in metres (m), and velocity in metres per second (m/s).

Frequency Remains Constant

When a sound wave passes from one medium to another (e.g., from air to water), its frequency does not change. The frequency of a sound wave is determined by the vibrating source that creates it. Since the source continues to vibrate at the same rate, the number of oscillations per second (frequency) remains the same as the wave moves into the new medium. This is a crucial point for understanding how other properties adjust.

Changes in Velocity and Wavelength

Because the frequency remains constant, any change in the velocity of a sound wave as it enters a new medium must directly affect its wavelength. If sound travels into a medium where its speed increases (e.g., from air to water), then for the frequency to stay constant, the wavelength must increase. Conversely, if sound travels into a medium where its speed decreases (e.g., from water to air), then the wavelength must decrease. This inter-relationship is a direct consequence of the wave equation (v = fλ) with 'f' being constant.

Examples of Medium Changes

Consider a sound wave moving from air into a solid wall. The speed of sound is much greater in solids than in air. Since the frequency doesn't change, the wavelength of the sound wave will significantly increase as it enters the wall. If the sound then passes from the wall back into air, its speed will decrease, and its wavelength will decrease back towards its original value in air. This principle applies universally for sound transmission across different materials.