Waves transfer energy and information from one place to another without transferring matter overall (no net transfer of matter). In mechanical waves, particles vibrate back and forth (oscillate) around their rest positions.
A floating cork bobs as water ripples pass; it does not travel across the tank with every crest. Sound can travel through air while the air particles vibrate locally.
In a transverse wave, vibrations are at right angles (perpendicular) to the direction of energy transfer. Examples include electromagnetic waves, waves on a string and seismic S waves.The two directions are perpendicular.
In a longitudinal wave, vibrations are back and forth along the direction of energy transfer (parallel to it). Sound in air and seismic P waves are longitudinal.
Longitudinal waves contain compressions, where particles are closer together, and rarefactions, where they are more spread out.Particles vibrate parallel to the propagation direction.
At GCSE, surface water ripples are represented as transverse waves. Real surface-water particle motion is more complex than a simple up-and-down line.
Sound needs a material to travel through, such as air, water or a solid. This material is called a medium, so sound cannot cross a vacuum. Electromagnetic waves can travel through a vacuum.
Wave measurements and equations
Wavelength λ is the distance between two corresponding points on neighbouring waves: points at the same stage, such as one crest to the next crest or one compression to the next. It is measured in metres (m).
Amplitude is the greatest distance a point on a wave moves from its rest position (its maximum displacement). Measure from the rest position to a crest or trough, not from crest to trough.Amplitude is measured from the rest position; wavelength joins matching points.
Frequency f is the number of complete waves (cycles) passing a point each second. It is measured in hertz (Hz). A frequency of 5 Hz means five complete waves, or cycles, per second.
Period T is the time for one complete wave cycle, measured in seconds (s). T = 1/f: a higher frequency means a shorter period.
Wave speed is how fast the wave travels, measured in m/s. A wavefront joins points at the same stage of a wave, such as the points along a ripple crest.
Use v = fλ for all waves: speed = frequency × wavelength. Rearrange to f = v/λ or λ = v/f.
A wave of frequency 4 Hz and wavelength 0.5 m travels at 2 m/s. Convert cm or mm to metres before using SI equations.
You can also use v = distance/time for a travelling pulse. Do not confuse the speed of a pulse with the sideways or up-and-down speed of the vibrating particles.
Measuring wave speed: core practical
In a ripple tank, a vibrating dipper produces water waves. Use a lamp and screen to see the wavefronts; measure the spacing across several wavelengths and divide by the number of intervals.
Find the frequency from the dipper setting or count its complete vibrations (oscillations) over a measured time: frequency = number of oscillations ÷ time. Then calculate v = fλ.
Use shallow, even water and small ripples; reflections from edges can interfere. Take repeats and avoid mistaking a moving shadow's scale for the actual wavelength.
For waves in a solid, a stretched string driven by a vibration generator is suitable. Identify adjacent nodes in a stationary-wave pattern: their spacing is half a wavelength, so λ = 2 × node spacing.
Keep the string tension and length controlled. Use the generator frequency and measured wavelength to calculate speed; stationary waves are produced by opposite travelling waves.
For a pulse on a rope or spring, measure a long known travel distance and time its passage. Slow pulses suit a stopwatch; short fast travel needs electronic timing or video.
To measure sound speed, use two microphones separated by a measured distance and an oscilloscope/data logger to measure the arrival-time difference of a sharp sound.Electronic timing resolves the short delay between the microphones.
An echo method uses speed = 2 × distance to reflector ÷ echo delay, because the sound travels out and back. Longer distances reduce relative timing error; repeat safely.
Choose equipment with sufficient time and distance resolution. State measured quantities, units, controls, repeats and likely sources of uncertainty.
Refraction and material interactions
Refraction happens when a wave crosses into a region where it travels at a different speed. Unless it meets the boundary along the normal, it also changes direction.
The boundary between two materials (media) is called the interface. The normal is an imaginary line at right angles to the boundary. Measure angles from the normal, not from the surface.
When a wave slows on entering a medium at an angle, it bends towards the normal. When it speeds up, it bends away from the normal.Angles are measured from the normal; at normal incidence there is no bend.
A wave meeting a boundary straight along the normal (normal incidence) does not change direction, although its speed and wavelength can change. Its frequency stays the same because the source still vibrates at the same rate.
Since v = fλ and frequency is unchanged, a lower speed means a shorter wavelength. Shallower water slows ripples compared with deeper water.
Materials can reflect, transmit, absorb or refract waves, with effects depending on wavelength. A transmitted wave need not keep the same speed as before.
Wave boundaries and echoes
At a material boundary a wave can be reflected back, transmitted into the next material, refracted as its speed changes, or absorbed with energy transferred to the material. These processes can occur together.
The frequency of a transmitted sound wave is set by the source and stays the same when it crosses a boundary. If its speed changes, wavelength changes in proportion because v = fλ.
(Higher tier) An echo travels to a reflecting object and back. One-way distance = wave speed × round-trip time ÷ 2; omitting the factor of two gives twice the correct distance (Higher tier calculation).The time interval for an echo corresponds to two journeys.
(Higher tier) Ultrasound is sound above 20000 Hz; infrasound is below 20 Hz. These definitions and the applications below are Higher-tier content in this specification.
(Higher tier) Ultrasound can be reflected at tissue boundaries to make a fetal image and can locate underwater objects with sonar. Different boundaries produce different reflected signals; ultrasound is not an ionising electromagnetic wave.
(Higher tier) Infrasound travels long distances and can monitor events such as volcanic activity. Analysis of seismic waves helps investigate Earth’s interior: their reflection, refraction and transmission reveal changes in materials.
Hearing and frequency response (Higher tier)
(Higher tier) Sound vibrations make the eardrum vibrate. Three small bones (the ossicles) pass the vibrations to the inner ear. The cochlea converts them into electrical signals, which travel along the auditory nerve.The ear converts mechanical vibrations into signals carried by the auditory nerve.
(Higher tier) The ear is sensitive to a limited range, approximately 20 Hz to 20000 Hz for a young healthy person. Age and damage can reduce this range; equal sound intensities at different frequencies are not necessarily heard equally loudly.
(Higher tier) In a microphone, air vibrations move a thin surface called a diaphragm. In a loudspeaker, the diaphragm vibrates and makes the air vibrate. These parts respond better to some frequencies than others, giving the device a limited frequency response.
(Higher tier) Protecting hearing involves limiting exposure to loud sound and using appropriate protection. Frequency is related to pitch, while loudness depends on intensity and the ear’s response; they are different quantities.
Watch SP4 · Waves · Topic 4 — Waves
Revise waves with this narrated video. Use the player controls to pause, seek, adjust the volume or mute. Turn English captions on or off using the captions menu.
Mr Kidman's Classroom