Sound, Waves and the Electromagnetic Spectrum

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What a wave is

A wave carries energy from place to place while the particles of the medium only vibrate about their mean positions. Mechanical waves such as sound and water waves need a medium; electromagnetic waves such as light do not. In a transverse wave the particles vibrate at right angles to the direction of travel, forming crests and troughs (a wave on a string, all electromagnetic waves); in a longitudinal wave they vibrate along it, forming compressions and rarefactions (sound in air). Only transverse waves can be polarised, which shows that light is transverse. Transverse waves cannot pass through the bulk of a liquid, which is why seismic S-waves do not cross the Earth's liquid outer core.

Frequency, wavelength and speed

Amplitude, the largest displacement of a particle, decides loudness, measured in decibels (dB). Frequency, the number of vibrations per second in hertz (Hz), decides pitch, and the time period is T = 1/f. Wavelength (λ) is the distance between two consecutive crests or compressions, and every wave obeys v = fλ: a 340 Hz note in air, where sound travels at about 340 m/s, has a wavelength of 1 m. Women's and children's voices have a higher pitch than men's; a mosquito's buzz is high-pitched and a lion's roar low-pitched but loud. Quality, or timbre, lets us tell a flute from a violin playing the same note equally loudly. Normal conversation is about 60 dB.

Infrasound and ultrasound

Humans hear from about 20 Hz to 20,000 Hz (20 kHz). Sound below 20 Hz is infrasound: earthquakes produce it before the main shock waves, and whales, elephants and rhinoceroses use it to communicate. Sound above 20 kHz is ultrasound: dogs can hear it, and bats, dolphins and porpoises produce it, bats to navigate and hunt in the dark by its echoes. Ultrasound is used in ultrasonography to see the foetus, liver and kidneys, in echocardiography to image the heart, to break kidney stones into fine grains, to detect cracks in metal blocks and to clean hard-to-reach parts.

Echo and SONAR

An echo is a reflected sound heard distinctly. The sensation of a sound lasts about 0.1 s in our brain, so the echo must return at least 0.1 s later; at 344 m/s (its speed in air at about 22 degrees C) sound covers 34.4 m in that time, so the reflecting surface must be at least 17.2 m away. In large halls repeated reflections make sound linger (reverberation), which is reduced with curtains and sound-absorbing boards. Multiple reflection is used in megaphones, horns, curved auditorium ceilings and the stethoscope, invented by René Laennec. SONAR (Sound Navigation And Ranging) sends ultrasonic pulses from a ship and times their echo to find the depth of the sea or to locate submarines and shipwrecks: depth = speed x time / 2. An echo returning in 2 s in sea water, where sound travels at about 1500 m/s, means a depth of 1500 m.

Speed of sound

Sound needs a medium and cannot travel through a vacuum, as the bell-jar experiment shows, so astronauts on the Moon talk by radio. It is fastest in solids, slower in liquids and slowest in gases: about 6000 m/s in steel (5960 m/s in NCERT's table), about 1500 m/s in water and about 331 m/s in air at 0 degrees C. In air it increases with temperature and humidity, while a change of pressure alone does not affect it. We see lightning before we hear thunder because light is nearly a million times faster, and the time gap tells how far away the storm is. An aircraft faster than sound is supersonic and produces a sonic boom.

Doppler effect

When a source of sound and a listener move relative to each other, the pitch heard changes: it rises as they approach and falls as they move apart, which is why a passing train's whistle drops in pitch. The Austrian physicist Christian Doppler explained it in 1842. Police speed guns, Doppler weather radar and Doppler ultrasound of blood flow use it, and the red shift in the light of distant galaxies shows that they are moving away from us.

The electromagnetic spectrum

Electromagnetic waves are transverse, need no medium and all travel at 3 x 10^8 m/s in vacuum; James Clerk Maxwell predicted them and Heinrich Hertz first produced radio waves in a laboratory. In order of increasing wavelength they are gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves and radio waves. Gamma rays come from nuclear reactions and are used to treat cancer and sterilise equipment; X-rays, discovered by Wilhelm Roentgen in 1895, show bones and scan baggage; ultraviolet rays from the Sun are mostly absorbed by the ozone layer, cause sunburn and help the skin make vitamin D; infrared is felt as heat and used in TV remote controls and night vision; microwaves cook food and carry radar and satellite signals; radio waves carry radio and television broadcasts.

Key facts

Transverse waves (crests and troughs): light and all EM waves, waves on a string. Longitudinal waves (compressions and rarefactions): sound in air. Only transverse waves can be polarised.
v = f x λ; frequency (Hz) decides pitch, amplitude decides loudness (dB), and quality (timbre) tells two instruments apart.
Audible range 20 Hz to 20 kHz; infrasonic below 20 Hz (earthquakes, whales, elephants); ultrasonic above 20 kHz (bats, dolphins; dogs can hear it).
Uses of ultrasound: ultrasonography, echocardiography, breaking kidney stones, detecting cracks in metal, cleaning small parts, SONAR.
An echo needs a 0.1 s gap, so the obstacle must be at least about 17.2 m away; SONAR depth = speed x time / 2.
Sound travels fastest in solids, then liquids, then gases; in air about 331 m/s at 0 degrees C, faster when hot or humid; there is no sound in vacuum, so astronauts use radio.
Doppler effect (Christian Doppler, 1842): an approaching source sounds higher in pitch; used in speed guns and weather radar, and the red shift shows galaxies receding.
EM spectrum by increasing wavelength: gamma, X-rays, ultraviolet, visible, infrared, microwave, radio; all travel at 3 x 10^8 m/s in vacuum.
X-rays: Roentgen, 1895; UV is mostly absorbed by ozone and helps make vitamin D; infrared: TV remote, night vision; microwaves: ovens, radar; gamma rays: cancer treatment.

Quick revision

Transverse: crests and troughs, light; longitudinal: compressions and rarefactions, sound; v = f λ; pitch = frequency, loudness = amplitude (dB); audible 20 Hz-20 kHz; infrasonic below, ultrasonic above (bats, SONAR, ultrasonography); echo needs 17.2 m; sound fastest in solids, none in vacuum, 331 m/s in air at 0 C; Doppler 1842; EM order: gamma, X, UV, visible, IR, microwave, radio; X-rays Roentgen 1895.

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