Question

A bat emits ultrasonic sound of frequency $100\, kHz$ in air. If this sound meets a water surface, the wavelengths of the reflected and transmitted sound are (Speed of sound in air $= 340\, ms^{-1}$ and in water $= 1500\, ms^{-1}$)

• A. $3.4\, mm$, $30 \,mm$
• B. $6.8\, mm$, $15 \,mm$
• C. $3.4\, mm$, $15 \,mm$
• D. $6.8\, mm$, $30 \,mm$

Answer 1

Answer: (C)

Here, $\upsilon = 100\,kHz = 100 \times 10^{3}\,Hz$
$= 10^{5}\, Hz = 10^{5}\, s^{-1}$
$v_{a }= 340 \,ms^{-1}, v_{w} = 1500\, ms^{-1}$
Frequency of both the reflected and transmitted sound remains unchanged.
Wavelength of reflected sound,
$\lambda_{a} = \frac{v_{a}}{\upsilon} = \frac{340\,ms^{-1}}{10^{5}\,s^{-1}}$
$= 34 \times 10^{-4}\,m$
$= 3.4 \times10^{-3}\,m = 3.4\,mm$
Wavelength of transmitted sound,
$\lambda_{w} = \frac{v_{w}}{\upsilon} = \frac{1500\,ms^{-1}}{10^{5}\,s^{-1}}$
$= 15 \times 10^{-3}\,m = 15\,mm$