Know that, in general, sound travels faster in solids than in liquids and faster in liquids than in gases

Cambridge IGCSE Physics 0625 – Topic 3.4 Sound

Learning Objective

Know that, in general, sound travels faster in solids than in liquids and faster in liquids than in gases.

1. What is Sound?

• Production – Sound is produced when a source (e.g. a plucked string, a vibrating speaker diaphragm, a struck tuning‑fork) vibrates and sets the surrounding medium into motion.
• Nature of the wave – It is a longitudinal mechanical wave: particles of the medium oscillate back‑and‑forth along the direction of travel.
• Human hearing range – 20 Hz – 20 kHz (below 20 Hz = infrasound, above 20 kHz = ultrasound).

2. How Fast Does Sound Travel?

Speed depends on two competing material properties:

• Elastic (stiffness) property – how quickly the medium restores its shape after being disturbed.
• Inertial (density) property – how much mass must be moved.

In general, the larger the ratio stiffness ÷ density, the faster the sound.

2.1. Mathematical Expressions

• Solid (Young’s modulus \$E\$): \(v_{\text{solid}}=\sqrt{\dfrac{E}{\rho}}\)
• Liquid (bulk modulus \$K\$): \(v_{\text{liquid}}=\sqrt{\dfrac{K}{\rho}}\)
• Ideal gas (using \$K=\gamma p\$): \(v_{\text{gas}}=\sqrt{\dfrac{\gamma p}{\rho}}=\sqrt{\gamma R T}\)

where \$\gamma\$ = ratio of specific heats, \$p\$ = pressure, \$\rho\$ = density, \$R\$ = specific gas constant, \$T\$ = absolute temperature (K).

2.2. Typical Speeds of Sound

3. Practical Determination of Sound Speed (Distance‑Time Method)

4. Amplitude, Frequency and Their Effects

• Amplitude → loudness: Larger amplitude vibrations produce a louder sound.
• Frequency → pitch: Higher frequency vibrations are heard as a higher pitch.

Example: Turning up the volume knob on a speaker increases amplitude (louder); playing a higher musical note increases frequency (higher pitch).

5. Echo

An echo is the reflection of a sound wave from a surface back to the source. The time interval \$\Delta t\$ between the original sound and its echo gives the distance \$d\$ to the reflecting surface:

\[

d = \frac{v\,\Delta t}{2}

\]

(where \$v\$ is the speed of sound in the medium).

6. Ultrasound

• Sound with frequency > 20 kHz.
• Common uses:

  • Medical imaging (e.g., fetal scans).
  • Industrial non‑destructive testing (detecting cracks).
  • Sonar for navigation and depth measurement.

7. Factors that Modify the Speed of Sound

• Solids – Material type (different \$E\$), temperature (both \$E\$ and \$\rho\$ change; speed usually falls when heated).
• Liquids – Temperature (affects \$K\$ and \$\rho\$), composition (e.g., dissolved salts increase \$\rho\$ and \$K\$), pressure (minor under everyday conditions).
• Gases – Temperature (speed ∝ √T), molecular weight (heavier gases → lower speed), humidity (water vapour lowers average molecular weight, raising speed), pressure (at constant \$T\$, speed is independent of \$p\$).

8. Example Calculation – Speed of Sound in Dry Air at 25 °C

Given \$\gamma = 1.40\$, \$R = 287\ \text{J kg}^{-1}\text{K}^{-1}\$, \$T = 298\ \text{K}\$:

\[

v = \sqrt{\gamma R T}= \sqrt{1.40 \times 287 \times 298}\;\approx\;346\ \text{m s}^{-1}

\]

9. Summary

• Sound requires a material medium and propagates as a longitudinal wave.
• Speed \$v = \sqrt{\text{stiffness}/\text{density}}\$ → solids > liquids > gases.
• Amplitude controls loudness; frequency controls pitch.
• Echoes are reflections; ultrasound (> 20 kHz) has specialised applications.
• Temperature, composition, and humidity modify \$v\$ in predictable ways.