Which quantity is directly proportional to the speed of sound, if the frequency is kept constant?
Wavelength
The speed of a sound wave is related to its frequency and wavelength by the wave equation \(v = f\lambda\), where v is the speed, f the frequency and \(\lambda\) the wavelength.
If the frequency f is kept constant, the equation gives \(\lambda = \frac{v}{f}\), so the wavelength changes in the same ratio as the speed. Therefore wavelength is directly proportional to the speed of sound at fixed frequency.
Frequency is the quantity held constant here, so it cannot vary with speed. Amplitude, and loudness which depends on amplitude, describe the energy carried by the wave and do not enter the relation between speed and frequency.
Check: a 500 Hz sound has \(\lambda = \frac{340}{500} = 0.68\) m in air at 340 m/s and \(\lambda = \frac{1500}{500} = 3\) m in water at 1500 m/s, so the wavelength rises in step with the speed.
Hence, Wavelength.
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