Know that a medium is needed to transmit sound waves

3.4 Sound – The Need for a Medium

Learning objective

Explain why sound waves require a material medium (solid, liquid or gas) to travel, describe how a vibrating source creates the disturbance, show how the disturbance is passed from particle to particle, and recognise that sound cannot propagate in a vacuum.

1. Production of sound by a vibrating source

• Definition: Sound is produced when a source vibrates, creating alternating regions of compression and rarefaction in a material medium.
• Examples:
  • A tuning‑fork vibrating back‑and‑forth.
  • A speaker diaphragm moving in and out.

2. Longitudinal nature of sound waves

• Sound is a mechanical longitudinal wave; the disturbance (compressions‑rarefactions) travels **parallel** to the direction of wave propagation.
• Particle‑model description:
  • Compression – particles are pushed together → region of higher density and pressure.
  • Rarefaction – particles are pulled apart → region of lower density and pressure.
  • Each particle oscillates about its equilibrium position; it does not travel with the wave.
  • The disturbance is handed from one particle to the next by successive collisions.

3. Why a material medium is essential

• The passage of compressions and rarefactions relies on particle interactions. Without particles there can be no pressure variations.
• In a vacuum there are no atoms or molecules to interact, so the wave cannot be sustained and dies out immediately.

4. Media and typical speeds of sound

Trend: sound travels fastest in solids (particles are tightly packed), slower in liquids, and slowest in gases. The speed \(v\) depends on the medium’s elasticity and its density \(\rho\); higher elasticity and lower density give a higher speed.

5. Quantitative factors influencing speed

• Elastic (bulk) modulus, \(B\) – resistance of the medium to compression.
• Density, \(\rho\) – mass per unit volume.
• For many media \( \displaystyle v \approx \sqrt{\frac{B}{\rho}} \)
• Temperature (gases only) – for an ideal gas \( \displaystyle v = \sqrt{\frac{\gamma RT}{M}} \) so speed increases with temperature.

6. Measuring the speed of sound (Core AO3 requirement)

Distance‑time (echo or two‑microphone) method

1. Place two microphones (or a speaker and a microphone) a measured distance \(d\) apart along a straight line.
2. Generate a short, sharp sound (e.g., a clap, starter pistol, or electronic pulse).
3. Record the time interval \(\Delta t\) between the arrival of the sound at the first and second microphone, or between the emitted pulse and its echo from a flat wall placed at a known distance.
4. Calculate the speed:
   • Two‑microphone method \( v = \dfrac{d}{\Delta t} \)
   • Echo method \( v = \dfrac{2d}{\Delta t} \)
5. Repeat several times, average the results and compare with the theoretical value from the formula in section 5.

Safety notes

• Do not use firearms or extremely loud devices near the ears – wear hearing protection.
• Keep the work area clear of obstacles to avoid tripping.
• If a loudspeaker is used, keep the volume at a safe level.

7. Amplitude, frequency, loudness & pitch

• Amplitude – maximum displacement of particles from equilibrium. Larger amplitude → larger pressure variation → **louder** sound (higher sound‑level, measured in decibels).
• Frequency, \(f\) – number of compressions‑rarefactions passing a point each second (Hz). Higher frequency → **higher pitch**.
• Amplitude does **not** affect pitch; frequency does **not** affect loudness (except at very high amplitudes where distortion may occur).

8. Ultrasound

Definition: Sound with a frequency above the upper limit of human hearing (generally > 20 kHz; many textbooks use > 25 kHz or > 40 kHz).

Typical applications

• Medical imaging (sonography) – high‑frequency waves reflect from internal structures.
• Non‑destructive testing – detecting cracks or faults in metal.
• Sonar – underwater navigation and ranging.
• Industrial cleaning – high‑frequency vibrations remove contaminants.

9. Connections to other parts of the syllabus

10. Summary – key points to remember

• Sound is a mechanical longitudinal wave; it is produced when a source vibrates, creating compressions and rarefactions.
• The disturbance is transmitted by particle collisions, so a material medium is required. In a vacuum sound cannot travel.
• Speed of sound depends on the medium’s elasticity and density; it is fastest in solids, slower in liquids, slowest in gases, and increases with temperature in gases.
• Amplitude determines loudness; frequency determines pitch.
• Ultrasound = sound with frequency > 20 kHz; widely used in medicine, industry and sonar.
• The speed can be measured safely with the distance‑time (or echo) method, and the result can be compared with the theoretical value \(v \approx \sqrt{B/\rho}\).