Speed of sound using stationary waves (PAG 12)
Determine the speed of sound in air by finding two successive resonant lengths of a closed air column.
Apparatus
- Resonance tube (adjustable length using inner sliding tube in water-filled outer tube)
- Tuning forks of known frequencies
- Metre rule
- Thermometer
Safety
- Strike tuning forks on a rubber pad only to avoid cracking.
- Handle glass tube carefully to avoid breakage.
Method
- Hold a vibrating tuning fork of frequency f just above the open end of the tube.
- Adjust column length until first loud resonance at $L_1$, then second resonance at $L_2$.
- Wavelength: $\lambda = 2(L_2 - L_1)$. Speed: $v = f\lambda$.
- Repeat for at least four tuning fork frequencies.
- Plot $\lambda$ vs $1/f$: straight line through origin, gradient $= v$.
Key Variables
Independent
Frequency f (via different tuning forks)
Dependent
Wavelength lambda
Controlled
Air temperature; Same tube diameter
Analysis and Results
- From two resonances: $\lambda = 2(L_2 - L_1)$, eliminating end correction.
- Plot $\lambda$ vs $1/f$: gradient $= v$.
- Compare v with the expected value at measured temperature: $v \approx 331 + 0.6T$ m s$^{-1}$ where T is in degrees C.
Common Errors
- Using only one resonance length (end correction introduces systematic error).
- Not striking tuning fork hard enough for a clear resonance.
- Not recording air temperature for comparison with the calculated speed.
Exam-style questions on this practical. Click Show mark scheme to reveal the answer after attempting each question.
Q14 marks
A 440 Hz tuning fork gives resonances at $L_1 = 18.2$ cm and $L_2 = 55.7$ cm. Calculate (a) the wavelength, (b) the speed of sound, and (c) the end correction.
Q22 marks
At 20 degrees C the expected speed of sound is approximately 343 m s$^{-1}$. The student measures 330 m s$^{-1}$. Suggest one reason for this discrepancy.