Question

A bat emits ultrasonic wave of frequency 30 KHz. If its speed is 350m/s and bats hear its echo after 0.6 sec

after emitting the, find how far is bat from obstacle and wave length of wave?

Answer 1

The speed of the wave $v$, its frequency $n$ and the wavelength of the wave $\lambda$ are related as,
$v=n\lambda$
Or,
$\lambda =\frac{v}{n}$
On substituting the values in the above equation we get,
$\lambda =\frac{350m/s}{30kHz}$
On converting kilohertz into hertz we get,
$$\begin{gathered} \lambda =\frac{350m/s}{30\times {10}^{3}Hz} \\ \lambda =0.0117m \\ \lambda =1.17\times 10-2m \end{gathered}$$

We know that the distance is the product of speed and time, so the distance between the bat and the obstacle is found as,
$s=vt$
On substituting the values we get,
$$\begin{gathered} s=\left(350m/s\right)\left(0.6s\right) \\ s=210m \end{gathered}$$