Speed of sound using an oscilloscope

Practical method

Aim

Measure the speed of sound in air by finding the wavelength of a sound of known frequency with two microphones and an oscilloscope.

Variables

Independent variable: microphone separation
Dependent variable: phase difference between the two traces
Control variables: signal frequency; air temperature.

Apparatus

• Signal generator and loudspeaker
• Two microphones
• Dual-trace oscilloscope
• Metre rule on the bench

Method

1. Connect the loudspeaker to a signal generator at 2.00 kHz and point it along a metre rule.
2. Place both microphones next to each other in front of the speaker and connect each to one channel of the oscilloscope; the traces are in phase.
3. Move one microphone away until the traces are in phase again; the distance moved is one wavelength.
4. Continue to several wavelengths and measure the total distance; divide by the number of wavelengths.
5. Calculate v = fλ and read the frequency from the oscilloscope time base.

Sample results

f = 2.00 kHz (checked from the trace: period 0.500 ms); air at 20 °C.

Analysis

λ = \(\dfrac{0.855}{5}\) = 0.171 m, so v = 2000 × 0.171 = 342 m s⁻¹, close to the accepted 343 m s⁻¹ at 20 °C.

Uncertainty

Judging the in-phase position is uncertain by about ±3 mm; over 5 wavelengths (0.855 m) this is 0.4%. The oscilloscope frequency reading (±1 division in 10) contributes about 1%.

Errors and improvements

Risk assessment

Common mistakes

• Assuming the signal generator dial is accurate.
• Counting half-wavelengths as wavelengths.
• Moving the loudspeaker instead of one microphone.

Worked analysis

The time base shows a period of 0.500 ms, so f = \(\dfrac{1}{0.500 \times 10^{-3}}\) = 2000 Hz. Five wavelengths span 0.855 m, so λ = 0.171 m and v = 2000 × 0.171 = 342 m s⁻¹.

Common misconception

The phase difference depends on the microphone separation, not on the loudness: traces come back into phase every full wavelength.