Physics · Lesson 16

Sound waves, resonance & musical notes

JAMBWAECNECO

What the syllabus asks

JAMB: Sound waves: properties, speed, echoes, resonance, vibrations in pipes and strings, musical sounds, beats

WAEC: Sound waves: production and propagation, need for a material medium, speed of sound in solids, liquids and gases, factors affecting speed, echoes and their uses, reverberation; characteristics of sound (pitch, loudness, quality); forced vibration and resonance, resonance tube, end correction; vibrations in strings and pipes (open and closed), harmonics and overtones, musical notes, beats

NECO: Sound waves: production and propagation, need for a material medium, speed of sound in solids, liquids and gases, factors affecting speed, echoes and their uses, reverberation; characteristics of sound (pitch, loudness, quality); forced vibration and resonance, resonance tube, end correction; vibrations in strings and pipes (open and closed), harmonics and overtones, musical notes, beats

What you will learn

Explain how sound is produced and why it needs a medium.
Use v = fλ and compare the speed of sound in different media.
Solve echo problems and describe uses of echoes.
Relate pitch, loudness and quality to frequency, amplitude and overtones.
Explain forced vibration and resonance, and use the resonance tube to find the speed of sound.
Find the frequencies of notes from strings and from open and closed pipes, and calculate beat frequency.

Key points

Sound: longitudinal wave from vibrations; needs a medium; no sound in a vacuum.
v = fλ; speed: solids > liquids > gases; rises with temperature, unaffected by pressure alone.
Echo: d = vt/2; uses include sonar, ultrasound scans and echolocation.
Pitch ↔ frequency; loudness ↔ amplitude; quality ↔ overtones.
Resonance: driving frequency = natural frequency → large amplitude.
Resonance tube: λ = 2(L₂ − L₁); e = (L₂ − 3L₁)/2.
Closed pipe: f₀ = v/4L, odd harmonics; open pipe: f₀ = v/2L, all harmonics.
String: f₀ = (1/2l)√(T/μ); beats = |f₁ − f₂|.

Start here: How sound is produced and travels

All sound comes from vibrating objects: the skin of a talking drum, the strings of a guitar, the air column in a flute, your vocal cords. As the object moves outward, it pushes air particles together (a compression); as it moves back, it leaves a region where they spread out (a rarefaction). These pressure changes pass from particle to particle.

Sound is a longitudinal mechanical wave: particles vibrate back and forth along the direction in which the wave travels.

Sound needs a medium. In the classic bell-jar experiment, an electric bell rings inside a glass jar. As a vacuum pump removes the air, the sound grows fainter until it is almost unheard, though the hammer is still seen striking the bell. Light passes through the vacuum, but sound does not. This is why astronauts on a spacewalk communicate by radio.

Worked example 16.1

Explain why the sound in the bell-jar experiment does not become completely silent.

No pump removes all the air; some particles remain.
Also, vibrations pass through the bell’s support into the jar and out.

Some air remains and the mounting conducts vibrations

⚠️ Common mistake: calling sound a transverse wave. In air, sound is always longitudinal.

Try it yourself. Why can a spaceship explosion not be heard from another ship in space?

Show solution

Space is (nearly) a vacuum: there is no medium to carry sound.

Watching sound move

You can model a sound wave with a long slinky spring stretched on a table. Push one end forward and back repeatedly: bunches of coils (compressions) and stretched regions (rarefactions) travel along the spring, but each coil only moves a little back and forth about its own position. The energy travels; the coils do not. In air, it is the same: when you speak to a friend across the classroom, no air from your mouth reaches their ear. The air molecules near you jostle their neighbours, and the pressure pattern moves across the room at about 340 metres every second.

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Practice questions

1. A sound of frequency 680 Hz has wavelength 0.5 m. Find its speed.

Show worked answer

340 m/s.

2. An echo from a cliff returns after 2.0 s (v = 330 m/s). How far is the cliff?

Show worked answer

330 m.

3. A closed pipe is 0.34 m long (v = 340 m/s). Find its fundamental.

Show worked answer

340/1.36 = 250 Hz.

4. An open pipe is 0.85 m long (v = 340 m/s). Find its first overtone.

Show worked answer

f₀ = 200 Hz; first overtone 400 Hz.

5. Resonances at 15.5 cm and 49.5 cm with a 500 Hz fork. Find v and e.

Show worked answer

λ = 68 cm; v = 340 m/s; e = (49.5 − 46.5)/2 = 1.5 cm.

Key words

Longitudinal wave: A wave whose particles vibrate along the direction of travel.
Compression: A region where particles are close together (high pressure).
Rarefaction: A region where particles are spread out (low pressure).
Echo: A reflected sound heard distinctly after the original.
Reverberation: Persistence of sound due to many overlapping reflections.
Pitch: How high or low a note sounds; determined by frequency.
Loudness: How strong a sound seems; related to amplitude and intensity.
Quality (timbre): The characteristic that distinguishes the same note from different instruments; due to overtones.
Natural frequency: The frequency at which a body vibrates freely.
Resonance: Large-amplitude vibration when the driving frequency equals the natural frequency.
Harmonic: A frequency that is a whole-number multiple of the fundamental.
Overtone: Any frequency above the fundamental produced by an instrument.

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