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Applications of Waves is taught in the note for Waves. Read it below and look for the section on this topic.

Waves

15 min read

Introduction to waves

A wave is a disturbance that carries energy from one place to another without carrying matter. In a transverse wave the particles vibrate at right angles to the direction the wave travels (light, water ripples, waves on a string). In a longitudinal wave they vibrate along the direction of travel (sound, a push on a spring).

Parts of a transverse waveA wave drawn as a sine curve. The amplitude is the maximum height of a crest above the rest position. The wavelength is the distance between two successive crests. The frequency is how many waves pass a point each second, and the wave speed is the frequency multiplied by the wavelength.amplitudewavelength λcresttroughv = f × λ
A longitudinal waveA row of vertical lines representing particles in a medium such as air or a spring. The particles move to and fro along the direction in which the wave travels, making regions pushed close together called compressions and regions spread apart called rarefactions. Sound is a longitudinal wave.direction of the wavecompressionrarefactioncompression
v = wave speed (m/s), f = frequency (hertz, Hz = waves per second), λ = wavelength (m), T = period (s). The speed of a wave depends on the medium; the frequency is set by the source.
Try itThe wave equation

Choose the frequency and wavelength. Find the wave speed and the period.

The dot moves up and down while the wave moves along.

Behaviour of waves

BehaviourWhat happens
ReflectionThe wave bounces off a barrier; the angle of incidence equals the angle of reflection
RefractionThe wave changes speed and direction when it passes into a medium of different depth or density; the wavelength changes, not the frequency
DiffractionThe wave spreads out round an edge or through a gap; most when the gap is about one wavelength wide
InterferenceTwo waves meet: crests add (constructive) or cancel crests with troughs (destructive)
Wave behaviour in a ripple tankThree panels of water waves. Reflection: straight waves hit a barrier and bounce back at the same angle. Refraction: waves slow down and bend when they pass into shallow water, and the wavelength gets shorter. Diffraction: waves spread out after passing through a gap, and spread most when the gap is about one wavelength wide.reflectionrefraction (shallow water)diffraction

Propagation of waves and sound waves

Sound is a longitudinal wave produced by a vibrating object. It needs a medium (solid, liquid or gas) and cannot travel in a vacuum. It travels fastest in solids and slowest in gases: about 330 m/s in air at 0 °C (340 m/s at 20 °C), 1 500 m/s in water and 5 000 m/s in steel. Sound speeds up as the temperature rises.

An echo is sound reflected from a hard surface. The depth of the sea or the distance to a cliff can be found from the time for the echo to return: sonar.

Echoes and sonarA ship sends a pulse of sound down to the sea bed. The sound reflects and returns as an echo. The depth is half the distance the sound travels, so depth equals speed times time divided by two. Bats and dolphins use echoes in the same way.pulseechodepth dd = (v × t) ÷ 2 (v ≈ 1 500 m/s in sea water)
Worked exampleDepth of the sea

A ship sends a pulse of sound and receives the echo 0.80 s later. How deep is the sea? (speed in sea water = 1 500 m/s)

  1. The sound travels down and back, so the total distance is 1 500 × 0.80 = 1 200 m.
  2. Depth is half of this.

Answer: The sea is 600 m deep.

Try itEcho distance

Choose the speed of sound and the time for an echo to return. Find the distance to the reflecting surface.

Musical sound

Pitch depends on the frequency: a higher frequency gives a higher note. Loudness depends on the amplitude. Quality (timbre) depends on the mixture of harmonics, which is why a guitar and a flute playing the same note sound different. Humans hear from about 20 Hz to 20 000 Hz. Above this is ultrasound, used in medical scans and in sonar.

Pitch and loudnessFour sound waveforms. A low pitch has few waves per second and a high pitch has many. A quiet sound has a small amplitude and a loud sound has a large amplitude. Pitch depends on frequency and loudness on amplitude.low pitch (low frequency)high pitch (high frequency)quiet (small amplitude)loud (large amplitude)

A stretched string or an air column can vibrate in standing waves, which have nodes (no movement) and antinodes (maximum movement). The fundamental frequency is the lowest; the overtones are whole-number multiples. A string of length L has a fundamental wavelength 2L. Resonance occurs when an object is forced to vibrate at its natural frequency and the amplitude becomes large.

Standing waves on a stringA string fixed at both ends can vibrate in patterns called harmonics. The fundamental has one loop and the wavelength is twice the string length. The second harmonic has two loops and the third has three. Points that never move are nodes, and points of largest movement are antinodes.fundamental: L = λ/22nd harmonic: L = λ3rd harmonic: L = 3λ/2nodeantinode (largest movement)

The electromagnetic spectrum and applications

Electromagnetic waves are transverse waves of changing electric and magnetic fields. They need no medium and all travel at 3 × 10⁸ m/s in a vacuum. They differ in wavelength and frequency.

The electromagnetic spectrumSeven bands of electromagnetic waves in order from radio waves with the longest wavelength and lowest frequency, through microwaves, infrared, visible light, ultraviolet and X-rays, to gamma rays with the shortest wavelength and highest frequency. All travel at the speed of light in a vacuum.RadiobroadcastingMicro-wavescooking, phonesInfraredremote controlsVisibleseeingUltravioletsterilisingX-raysmedical imagesGammatreating cancerlonger wavelength, lower frequencyshorter wavelength, higher frequencyAll travel at 3 × 10⁸ m/s in a vacuum
WaveUseDanger
Radio wavesBroadcasting, communicationLow
MicrowavesCooking, mobile phones, radarHeat tissue at high power
InfraredRemote controls, heaters, thermal imagingSkin burns
Visible lightSeeing, photography, optical fibresVery bright light damages the eye
UltravioletSterilising, security marks, vitamin DSunburn and skin cancer
X-raysMedical imaging, airport securityDamage cells
Gamma raysSterilising food, treating cancerVery harmful
Check yourself Which wave is longitudinal?
Check yourself A wave has a frequency of 5 Hz and a wavelength of 4 m. Its speed is…
Check yourself When a wave passes from deep to shallow water, which quantity does not change?

Key terms

Wavelength
The distance between two successive crests.
Frequency
The number of waves passing a point each second.
Diffraction
The spreading of a wave through a gap or round an obstacle.
Resonance
Large vibration when a system is driven at its natural frequency.

Summary

  • Waves carry energy; transverse and longitudinal; v = fλ.
  • Reflection, refraction, diffraction and interference are wave behaviours.
  • Sound needs a medium; echoes give distance d = vt ÷ 2; pitch ↔ frequency, loudness ↔ amplitude.
  • All electromagnetic waves travel at 3 × 10⁸ m/s in a vacuum.
Electromagnetic Spectrum