Question

Challenge: a sound wave with a frequency of 100.0 Hz travels in water with a speed of 1,500 m/s and then travels in air with a speed of 340 m/s. Approximately how many times larger is the wavelength in water than in air?

Answer 1

Concept: The frequency won't change in water or in air.

Since wavelength x frequency = speed, wavelength is proportional to speed.

So, Middle C has a longer wavelength in water than in air.

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Answer 2

Answer: The correct answer is 44 times.

Explanation:

The expression of the wavelength in terms of the frequency is as follows;

$\lambda =\frac{v}{f}$

Here, $\lambda$  is the wavelength, f is the frequency and v is the speed of the sound.

It is given in the problem that a sound wave with a frequency of 100.0 Hz travels in water with a speed of 1,500 m/s and then travels in air with a speed of 340 m/s.

Calculate the wavelength in water.

$\lambda =\frac{v}{f}$

Put f= 1000 Hz and v= 1500 m/s.

$\lambda =\frac{1500}{1000}$                     .......... (1)

Calculate the wavelength in air.

$\lambda =\frac{v}{f}$

Put f= 1000 Hz and v= 340 m/s.

$\lambda =\frac{340}{1000}$                       ........... (2)

Divide equation (1) by (2) to compare the wavelength of the wave in water with the wavelength in air. The wavelength in water is approximately 44 times the wavelength in air.