7 min readConcept sheetPart I (1 mark) and Part II (2 marks): definitions, frequency ranges and v = nλ

Sound as a longitudinal wave

Sound is a longitudinal mechanical wave: air particles vibrate back and forth along the direction of travel, forming compressions and rarefactions. It needs a medium.

Wave equationv = nλ (n = frequency, λ = wavelength)

Audible range20 Hz to 20,000 Hz

Infrasonic and ultrasonicBelow 20 Hz; above 20,000 Hz

MediumNeeded; sound cannot travel through vacuum

Longitudinal vs transverse waves

Longitudinal waveThe particles of the medium vibrate parallel to the direction in which the wave travels. They form compressions (crowded regions of high pressure) and rarefactions (spread-out regions of low pressure). Example: sound in air.

Transverse waveThe particles vibrate perpendicular (at right angles) to the direction of the wave. They form crests and troughs. Example: ripples on a pond, a wave on a stretched string.

Sound is a mechanical wave: it needs a medium (solid, liquid or gas) to travel. Light is not; it can cross empty space.

How sound travels

Strike a tuning fork. Its prong moves forward and pushes the layer of air next to it. The air is squeezed, and a compression forms. The prong moves back. The air layer spreads out, and a rarefaction forms. The prong keeps vibrating, so compressions and rarefactions move outward one after another. The air particles only vibrate about their own positions. It is the energy that travels to your ear, not the air itself. The distance between two neighbouring compressions (or two neighbouring rarefactions) is the wavelength (λ). The number of vibrations per second is the frequency (n), measured in hertz (Hz). The speed of the wave is v = nλ.

Try this: sound needs a medium (bell jar experiment)

1
Hang an electric bell inside a glass bell jar joined to a vacuum pump.
2
Switch on the bell. You see the hammer strike the gong and hear the ring clearly.
3
Start pumping out the air. The sound becomes fainter and fainter.
4
When almost all the air is removed, you still see the hammer move but hear almost nothing.
5★
Conclusion: sound needs a material medium to travel; it cannot pass through a vacuum.

★ key step

Sound by frequency

Type	Frequency	Examples
Infrasonic	Below 20 Hz	Earthquakes, elephants, whales
Audible (sonic)	20 Hz to 20,000 Hz	Human speech, music, temple bells, traffic
Ultrasonic	Above 20,000 Hz	Bats and dolphins; dogs can hear some; used in ultrasound scanning

Worked example: v = nλ

Problem

A tuning fork of frequency 512 Hz is struck in air where sound travels at 340 m/s. Find the wavelength. Also find the frequency of a sound whose wavelength in air is 1.7 cm.

Working

Formula: v = nλ, so λ = v/n.
λ = 340 m/s ÷ 512 Hz ≈ 0.66 m (rounded to 2 decimal places).
Second part: λ = 1.7 cm = 0.017 m. Formula: n = v/λ.
n = 340 m/s ÷ 0.017 m = 20,000 Hz.
This is the upper limit of human hearing.

Answer

λ ≈ 0.66 m; n = 20,000 Hz (20 kHz)

In real life

Elephants in the Mudumalai forest call one another with infrasonic rumbles that we cannot hear. In hospitals, an ultrasound scan uses sound far above our hearing range to see inside the body.

Exam angle

1 marks: “Sound waves in air are ___ waves.” Longitudinal.

2 marks: “What are infrasonic and ultrasonic waves? Give one example of each.” Infrasonic: below 20 Hz, e.g. waves from earthquakes or elephants. Ultrasonic: above 20,000 Hz, e.g. sounds made by bats.

4 marks: “Explain how sound travels through air as compressions and rarefactions. Find the wavelength of a 256 Hz sound in air (v = 340 m/s).” A vibrating source pushes and pulls air layers into compressions and rarefactions; energy moves while particles vibrate in place. λ = 340 ÷ 256 ≈ 1.33 m.

Remember it

Compression = Crowded, Rarefaction = Roomy. Human hearing: 20 to 20,000 Hz.