A loudspeaker gives (frequency in Hz, wavelength in m) measurements (250, 1.36), (300, 1.13), (350, 0.97), (400, 0.85), (450, 0.76). (a) Estimate sound speed from two readings. (b) Test another reading for consistency. (c) Explain frequency and wavelength changes on entering warmer air. (d) Describe a stationary-wave wavelength method and uncertainty reduction.

Question

Accepted Answer

Sound speed about 340 m/s; 350 Hz gives 339.5 m/s and is consistent. Source frequency stays fixed while speed and wavelength depend on medium. Use v = fλ. The 250 Hz reading gives 250 × 1.36 = 340 m/s; the 400 Hz reading gives 400 × 0.85 = 340 m/s. At 350 Hz, v = 350 × 0.97 = 339.5 m/s, only 0.5 m/s different. This is consistent with measurement precision rather than evidence of a speed change. Source oscillation fixes frequency, which remains continuous across a boundary. If wave speed changes in warmer air, wavelength changes because λ = v/f. Create resonance in a tube or reflection from a wall and locate successive nodes with a microphone. Adjacent nodes are λ/2 apart, so double the spacing. Measure across several node gaps and divide by their number; repeat in both directions, keep frequency and temperature controlled and reduce unwanted room reflections.

Sound speed from wavelength evidence

What a complete response should do

Sound wavelength data

How did this one feel?

Sound wavelength data — supplied values
Frequency / Hz	Wavelength / m
250	1.36
300	1.13
350	0.97
400	0.85
450	0.76