Year 11 Physics Module 3 ⏱ ~40 min 5 MC · 3 Short Answer Lesson 9 of 18

Sound as a Mechanical Wave

In 1816, Pierre-Simon Laplace lectured at École Polytechnique Paris and corrected Newton's 1687 speed-of-sound prediction. Newton had assumed isothermal compression and calculated 280 m/s for air; Laplace showed that rapid compressions are adiabatic and introduced γ = C_p/C_v = 1.4 for air, giving v = √(γP/ρ) = 331 m/s, within 0.5% of the experimentally measured value at 0°C.

Today's hook: In 1816 at École Polytechnique Paris, Pierre-Simon Laplace showed why Newton's 280 m/s speed-of-sound prediction was wrong. Newton had assumed air is compressed isothermally; Laplace recognised that compressions happen too fast for heat to escape, they are adiabatic. Inserting γ = 1.4 gives 331 m/s, within 0.5% of measured. The fix works because sound is a longitudinal mechanical wave: compressions and rarefactions travel by particle-to-particle interaction, not radiation.

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Warm up first

Three quick questions from earlier lessons. Pulling old material back to mind before you learn something new makes the new material stick better, so this is not busywork.

Before you read, predict

Could you hear a loud explosion in the vacuum of space? Explain using what you know about waves. Write your prediction.

Warm-up, in a sound wave, air particles oscillate in which direction relative to wave travel?

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Learning Intentions

goals

Know

Sound is a longitudinal mechanical wave
Requires a medium; cannot travel in a vacuum
Compressions (high pressure) and rarefactions (low pressure)

Understand

How a vibrating source creates compressions and rarefactions
Why sound travels faster in solids/liquids than in gases
How frequency relates to pitch and amplitude to loudness

Can Do

Draw and label a longitudinal wave model of sound
Identify compression and rarefaction regions
Calculate wavelength/frequency/speed using $v = f\lambda$

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Key Terms

vocab

Longitudinal waveA wave where particles oscillate parallel to the direction of energy transfer. Sound is the key example.

CompressionA region of higher-than-normal pressure/density in a sound wave, corresponds to a crest in a transverse model.

RarefactionA region of lower-than-normal pressure/density in a sound wave, corresponds to a trough in a transverse model.

Speed of sound in airApproximately 340 m/s at 20°C. Faster in liquids and solids. Cannot propagate in a vacuum.

Cross-lesson links: L01–L08 established general wave properties (type, speed, superposition, diffraction, standing waves); this lesson applies all of those to sound specifically. L10 (intensity and decibels) builds directly on the compression/rarefaction amplitude model introduced here. L11 (standing waves in pipes) uses the 340 m/s speed of sound to calculate harmonic frequencies.

Misconceptions to fix

✗ Wrong: Sound particles move forward with the wave.

✓ Right: Particles only oscillate back and forth about their equilibrium positions. The wave pattern (not matter) moves forward.

✗ Wrong: Higher density always means slower sound.

✓ Right: Sound speed depends on elasticity/bulk modulus AND density. Steel is denser than air but sound travels ~17× faster through it because steel is far more elastic.

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The Longitudinal Wave Model of Sound

Core Content

The Longitudinal Wave Model of Sound

+5 XP

In 1816, Laplace is at the blackboard in Paris. He strikes a tuning fork. The prong pushes forward, squashing the air molecules immediately in front of it into a high-pressure compression. Those crowded molecules push their neighbours, who push theirs, a pressure ripple races outward at 331 m/s. Between each compression is a rarefaction where the returning prong pulled the air, leaving it momentarily thin. The room hears a pure tone: a succession of compressions and rarefactions arriving at 440 times per second.

A vibrating source (e.g. a speaker cone) pushes and pulls the adjacent air particles. Those particles push their neighbours, and so on. This creates alternating regions of compression and rarefaction that travel outward as a longitudinal wave. The particles themselves do not travel, they oscillate back and forth about fixed positions.

Sound property	Wave property
Pitch (high/low)	Frequency (high/low)
Loudness (loud/quiet)	Amplitude (large/small)
Tone colour (timbre)	Waveform shape (harmonics)

Sound is a longitudinal mechanical wave: particle oscillations are parallel to wave travel, creating compressions (high pressure) and rarefactions (low pressure). Speed in air ≈ 340 m/s (20°C); cannot propagate in a vacuum. Pitch corresponds to frequency; loudness corresponds to amplitude.

Pause, copy the highlighted sound model definition into your book before moving on.

A sound wave in air has a frequency of 680 Hz. Using $v_{sound} = 340$ m/s, the wavelength is:

Sound cannot travel through a vacuum because it requires particles to oscillate.

Higher pitch corresponds to a larger amplitude in a sound wave.

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Activity 2, Draw a Sound Wave

Activities

Activity 2, Draw a Sound Wave

ApplyBand 3

Draw a longitudinal wave model of sound showing at least 2 compressions and 2 rarefactions. Label: compression, rarefaction, wavelength, and the direction of particle oscillation.

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Activity 3, Speed Comparison

UnderstandBand 3

The speed of sound in various media: air (20°C) = 340 m/s; water = 1480 m/s; steel = 5960 m/s. Explain the trend using the concept of elasticity and particle separation.

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Activity 4, Calculation Practice

ApplyBand 4

Use $v = f\lambda$ to answer:

A 440 Hz note in air (340 m/s). Find $\lambda$.
Sound of $\lambda$ = 0.25 m in air (340 m/s). Find $f$.
A 200 Hz sound in water (1480 m/s). Find $\lambda$.

Which of the following is NOT a property of a sound wave in air?

In a compression region of a sound wave, the air pressure is:

A student increases the loudness of a sound without changing the pitch. What wave property changes?

✓

Show what you have learned

Multiple Choice, sound as a mechanical wave

+5 XP

Short Answer, 10 marks

+5 XP

UnderstandBand 3(3 marks) 1. Describe the model of sound as a longitudinal wave in air. In your answer explain what compressions and rarefactions are.

ApplyBand 4(3 marks) 2. Calculate the wavelength of a 500 Hz sound in (a) air (340 m/s) and (b) water (1480 m/s). Show all working.

AnalyseBand 5(4 marks) 3. Explain why sound travels faster through steel (5960 m/s) than through air (340 m/s), even though steel is much denser. Reference elasticity in your answer.

Show all answers

Activity 4 Calculations

1. $\lambda = 340/440 = 0.77$ m 2. $f = 340/0.25 = 1360$ Hz 3. $\lambda = 1480/200 = 7.4$ m

Short Answer, Model Answers

Q1 (3 marks): Sound is a longitudinal wave because particles oscillate parallel to the direction of energy transfer. A vibrating source pushes air molecules together (compression = higher pressure region) then pulls back creating a rarefaction (lower pressure region). This alternating pattern propagates through the air as the wave.

Q2 (3 marks): (a) $\lambda = v/f = 340/500 = 0.68$ m. (b) $\lambda = 1480/500 = 2.96$ m.

Q3 (4 marks): Sound speed is determined by $v = \sqrt{E/\rho}$ where $E$ is the bulk modulus (elasticity) and $\rho$ is density. Steel is highly elastic, it resists compression strongly and springs back quickly. Although steel's density is ~7800 kg/m³ compared to air's ~1.2 kg/m³, its bulk modulus is ~170 GPa versus air's ~140 kPa, a factor of over 10⁶ greater. The ratio $E/\rho$ is much larger for steel, giving a higher wave speed.

✓

Retrieve, reflect and finish

Check what actually stuck

How did your thinking change?

In 1816, Pierre-Simon Laplace corrected Newton's 280 m/s by recognising that sound compressions are adiabatic (γ = 1.4 for air), giving 331 m/s, within 0.5% of experiment. The correction works because sound is a longitudinal mechanical wave: compressions require particles to push neighbours, so no medium means no sound.

Your Think First prediction about the space explosion was correct: you cannot hear it. The Laplace story makes the reason concrete, without air molecules (or any particles) to form compressions and rarefactions, the longitudinal wave cannot propagate. Light from the explosion travels as a transverse electromagnetic wave and needs no medium.

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← Lesson 8: Progressive vs Standing Waves Next: Sound Intensity and Beats →

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