When a wave travels from one medium to another medium, the wavelength changes but not the frequency. The wavelength of the sound disturbance 30 cm in air and of the wave velocity is 340 m/s. What will be the wavelength of the disturbance in helium and water? The speed of sound in helium is 970 m/s and 1450 m/s in water.

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Solution

We know frequency= $\frac{V e l o c i t y}{W a v e l e n g t h}$
If frequency is constant then, $\frac{V e l o c i t y i n a i r}{W a v e l e n g t h i n a i r} = \frac{V e l o c i t y i n h e l i u m}{W a v e l e n g t h i n h e l i u m}$
$\Rightarrow \frac{340}{0.30} = \frac{970}{W a v e l e n g t h i n h e l i u m}$
$\Rightarrow W a v e l e n g t h i n h e l i u m = 0.855 m = 85.5 c m$
$\frac{V e l o c i t y i n a i r}{W a v e l e n g t h i n a i r} = \frac{V e l o c i t y i n w a t e r}{W a v e l e n g t h i n w a t e r}$
$\frac{340}{0.30} = \frac{1450}{W a v e l e n g t h i n w a t e r}$
Wavelength in water = 1.279 m = 127.9 cm

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