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 m `s^(-1)` and in water = 1500 m `s^(-1)` )

Options

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

C

Explanation

Here, `v = 100" kHz" = 100 xx 10^(3)" Hz" = 10^(5)" Hz" = 10^(5)" s"^(-1)`
`v_a = 340" m s"^(-1), v_w = 1500"m s"^(-1)`
Frequency of both the reflected and transmitted sound remains unchanged.
Wavelength of reflected sound,
`lambda_1 = (v_a)/( upsilon) = (340"m s"^(-1) )/( 10^(5)" s"^(-1)) = 34 xx 10^(-4)" m"`
`= 3.4 xx 10^(-3)"m" = 3.4`mm
Wavelength of transmitted sound,
`lambda_w = (v_w)/( upsilon) = (1500"m s"^(-1) )/( 10^(5)" s"^(-1) ) = 15 xx 10^(-3)" m" = 15" mm"`