Speed of sound from stationary waves

Practical method

Aim

Measure the speed of sound by locating the nodes of a stationary sound wave formed between a loudspeaker and a reflecting board.

Variables

Independent variable: frequency of the sound
Dependent variable: distance between adjacent nodes
Control variables: air temperature; positions of speaker and reflector.

Apparatus

• Signal generator and loudspeaker
• Flat reflecting board
• Microphone and oscilloscope (or sound meter)
• Metre rule on the bench

Method

1. Point the loudspeaker at a reflecting board about 1 m away; the incident and reflected waves form a stationary wave.
2. Move a microphone along the line between them and watch the oscilloscope: the amplitude is minimum at nodes and maximum at antinodes.
3. Measure the distance across several node spacings and divide to find the spacing between adjacent nodes \(\dfrac{\lambda }{2}\).
4. Calculate λ and v = fλ. Repeat at several frequencies.
5. Plot λ against \(\dfrac{1}{f}\): gradient = v.

Sample results

Air at 20 °C.

Analysis

At 2000 Hz, five node spacings span 0.428 m, so \(\dfrac{\lambda }{2}\) = 0.0856 m and λ = 0.171 m: v = 342 m s⁻¹. λ against \(\dfrac{1}{f}\) is a straight line through the origin with gradient 342 m s⁻¹.

Uncertainty

Each node position is judged to about ±3 mm; across five spacings (0.428 m) this is 1.4%. Lower frequencies give longer distances and smaller percentage uncertainty, but fewer nodes fit in the space.

Errors and improvements

Risk assessment

Common mistakes

• Taking the node spacing as a full wavelength.
• Measuring only one node spacing.
• Ignoring temperature when comparing with the accepted value.

Worked analysis

At 2000 Hz, 5 node spacings = 0.428 m, so spacing = 0.0856 m = \(\dfrac{\lambda }{2}\). λ = 0.171 m and v = 2000 × 0.171 = 342 m s⁻¹.

Common misconception

Adjacent nodes are half a wavelength apart, not a full wavelength.