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.