Question

Ultrasonic sound of frequency $100kHz$ emitted by a bat is incident on a water surface. Calculate the wavelength of reflected sound and transmitted sound? (speed of sound in air $340m{s}^{-1}$)

Answer 1

Wavelength of incident wave ${\lambda }_i=\frac{v}{\nu }$
$⟹{\lambda }_i=\frac{340}{100\times 1000}=3.4\times {10}^{-3}m=3.4mm$
Since the reflected sound travels in same medium as the incident sound wave, thus wavelength of reflected sound wave is same as that of incident wave i.e. $3.4mm$.
Refractive index of water $n=1.33$
So, wavelength of transmitted wave ${\lambda }_t=\frac{{\lambda }_i}{n}$
$\therefore$ ${\lambda }_t=\frac{3.4}{1.33}=2.55mm$