17  Sound Waves

17.1 Syllabus inquiry question

  • How do sound waves carry energy and information?
Feynman Insight

From The Feynman Lectures on Physics, Vol I, Chapter 31:

Sound is a pressure wave in a material. The physics is in how compressions and rarefactions propagate through the medium.

17.2 Learning Objectives

  • Describe sound as a longitudinal wave.
  • Relate frequency to pitch and amplitude to loudness.
  • Calculate sound intensity and apply inverse square behaviour.
  • Interpret speed of sound in air.

17.3 Content

17.3.1 Nature of Sound

Sound waves are longitudinal pressure waves. The medium (usually air) oscillates parallel to the wave’s direction of travel.

Key features: - Compressions: Regions of high pressure (molecules pushed together) - Rarefactions: Regions of low pressure (molecules spread apart) - Wavelength: Distance between successive compressions (or rarefactions)

Sound Requires a Medium

Sound cannot travel through a vacuum. It needs a medium (solid, liquid, or gas) to propagate.

17.3.2 Interactive: Longitudinal Wave Visualization

Sound as a pressure wave:

In this representation, the vertical displacement shows how far particles are from their equilibrium positions.

17.3.3 Speed of Sound

The speed of sound depends on the medium:

Medium Speed (m/s) Reason
Air (20°C) 343 Gas molecules far apart
Water 1480 Liquid molecules closer
Steel 5960 Solid atoms tightly bonded

In air, temperature affects speed: \[v \approx 331 + 0.6T\]

where \(T\) is temperature in °C.

17.3.4 Pitch and Frequency

Pitch is the perceived highness or lowness of a sound.

Property Physical Quantity Range for Humans
Low pitch Low frequency 20 Hz (bass)
High pitch High frequency 20,000 Hz (treble)
Musical Notes

Frequency doubles for each octave. Middle C is about 262 Hz; the C one octave higher is 524 Hz.

17.3.5 Interactive: Different Frequencies

Compare low and high frequency waves:

Higher frequency = shorter wavelength = higher pitch.

17.3.6 Loudness and Amplitude

Loudness is the perceived intensity of sound.

  • Larger amplitude → louder sound
  • Smaller amplitude → softer sound

However, our perception of loudness is logarithmic (decibel scale).

17.3.7 Intensity and the Inverse Square Law

Intensity is power per unit area: \[I = \frac{P}{A}\]

For a point source radiating uniformly: \[I = \frac{P}{4\pi r^2}\]

Inverse Square Law

When distance doubles, intensity decreases to one-quarter.

\[\frac{I_2}{I_1} = \left(\frac{r_1}{r_2}\right)^2\]

17.3.8 Interactive: Intensity vs Distance

Visualizing how intensity decreases with distance:

17.4 Worked Examples

17.4.1 Example 1: Sound intensity

A speaker outputs 12 W uniformly. Find the intensity 2.0 m away.

Solution:

  1. Use the intensity formula: \(I = \frac{P}{4\pi r^2}\)

  2. Substitute: \(I = \frac{12}{4\pi \times 2.0^2} = \frac{12}{50.3} = 0.24\) W/m²

  3. Intensity is 0.24 W/m² at 2.0 m

17.4.2 Example 2: Frequency from wavelength

Sound travels at 340 m/s with wavelength 0.85 m.

Solution:

  1. Use the wave equation: \(f = v/\lambda\)

  2. Substitute: \(f = 340/0.85 = 400\) Hz

  3. The pitch corresponds to 400 Hz (about G4 in music)

17.4.3 Example 3: Change in intensity with distance

A listener moves from 1.0 m to 3.0 m from a speaker. Compare the intensities.

Solution:

  1. Intensity ratio: \(\frac{I_2}{I_1} = \left(\frac{r_1}{r_2}\right)^2 = \left(\frac{1.0}{3.0}\right)^2 = \frac{1}{9}\)

  2. Intensity at 3.0 m is one-ninth of the intensity at 1.0 m

  3. The sound is significantly quieter at 3.0 m

17.4.4 Example 4: Speed of sound at different temperatures

Find the speed of sound in air at 25°C.

Solution:

  1. Use the temperature formula: \(v \approx 331 + 0.6T\)

  2. Substitute: \(v = 331 + 0.6 \times 25 = 331 + 15 = 346\) m/s

  3. Sound travels at about 346 m/s at 25°C

17.5 Common Misconceptions

Common Misconceptions

  • Misconception: Sound travels in a vacuum. Correction: Sound requires a material medium. It cannot propagate through empty space.

  • Misconception: Higher pitch means higher amplitude. Correction: Pitch depends on frequency, not amplitude. Loudness depends on amplitude.

  • Misconception: Intensity halves when distance doubles. Correction: Intensity decreases by a factor of four (inverse square law).

  • Misconception: Sound travels at the same speed in all materials. Correction: Speed depends on the medium—faster in solids and liquids than gases.

17.6 Practice Questions

17.6.1 Easy (2 marks)

Explain why sound cannot travel in space.

  • Space is a vacuum / has no matter (1)
  • Sound requires a medium to propagate (1)

Answer: Space is a vacuum. Sound is a mechanical wave that requires a medium (solid, liquid, or gas) to propagate. Without particles to vibrate, sound cannot travel.

17.6.2 Medium (4 marks)

A sound wave has frequency 250 Hz in air where the speed of sound is 330 m/s. Find the wavelength.

  • Use \(\lambda = v/f\) (2)
  • Correct value: \(\lambda = 330/250 = 1.32\) m with units (2)

Answer: 1.32 m (or 1.3 m)

17.6.3 Hard (5 marks)

A 20 W siren radiates uniformly. Find the intensity at 5.0 m. If the distance doubles, by what factor does the intensity change?

  • Use \(I = P/(4\pi r^2)\) (2)
  • Correct intensity: \(I = 20/(4\pi \times 25) = 0.064\) W/m² (1)
  • Apply inverse square: factor = \((5/10)^2 = 1/4\) (1)
  • Intensity decreases by factor of 4 (1)

Answer: Intensity at 5.0 m = 0.064 W/m². When distance doubles, intensity decreases by a factor of 4.

17.7 Multiple Choice Questions

Test your understanding with these interactive questions:

17.8 Summary

Key Takeaways
  • Sound is a longitudinal pressure wave of compressions and rarefactions
  • Sound requires a medium—it cannot travel through a vacuum
  • Frequency determines pitch; amplitude affects loudness
  • Intensity: \(I = P/A\); for a point source: \(I = P/(4\pi r^2)\)
  • Inverse square law: doubling distance reduces intensity by factor of 4

17.9 Self-Assessment

Check your understanding:

After studying this section, you should be able to: