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.
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?
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 $v = f\lambda$
Core Content
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.
Activities
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.
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.
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?
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.
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.