Question

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

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

Answer 1

The correct option is C $3.4mm,15mm$

Here,

$\upsilon =100kHz=100\times {10}^{3}Hz$

$={10}^{5}Hz={10}^5{s}^{-1}$

${\nu }_a=340m{s}^{-1},{\nu }_w=1500m{s}^{-1}$

Frequency of both the reflected and transmitted sound remains unchanged.

Wavelength of transmitted sound,

${\lambda }_a=\frac{{\nu }_a}{\upsilon }=\frac{340m{s}^{-1}}{{10}^5{s}^{-1}}=34\times {10}^{-4}m$

$=3.4\times {10}^{-3}m$

Wavelength of transmitted sound,

${\lambda }_w=\frac{{\nu }_w}{\upsilon }=\frac{1500m{s}^{-1}}{{10}^5{s}^{-1}}=15\times {10}^{-3}m=15mm$