Question

A 440 Hz sound wave in 20°C air propagates into the water of a swimming pool. What are the wave’s (a) frequency and (b) wavelength in the water?

Short answer

Part a

The frequency of the wave is $440Hz$.

Part b

The wavelength of the sound wave in water is$3.4m$.

Step-by-step solution

Given information

The frequency of a sound wave in the air at$20°C$is$f=440Hz$.

Part a

As the harmonic oscillators in one medium excite the oscillators in another medium, the frequency must remain the same.

Therefore, the frequency of the wave is$440Hz$.

Part b

Speed of sound in water is $v=1480m/s$.

The relation between wavelength, frequency, and speed of the wave is given by $\lambda =\frac{v}{f}$.

Substitute the given values

$$\begin{gathered} \lambda =\frac{1480}{440} \\ \approx 3.4m \end{gathered}$$

Therefore, the wavelength of the sound wave in water is$3.4m$.