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Question : 6 of 27
Marks: +1, -0
A bat emits ultrasonic sound of frequency 1000 kHz in air. If this sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound? Speed of sound in air is 340 ms−1\mathrm{m s}^{-1} and in water 1486 ms−1\mathrm{m s}^{-1}.
Solution:  
Here, υ=1000 kHz\upsilon = 1000\ \mathrm{kHz} =1000×103 Hz=106 Hz= 1000 \times 103\ \mathrm{Hz} = 106\ \mathrm{Hz};
speed of sound in air, va=340 ms−1v_a = 340\ \mathrm{m s}^{-1};
speed of sound in water, vw=1,486 ms−1v_w = 1{,}486\ \mathrm{m s}^{-1}
(a) The reflected sound : After reflection, the ultrasonic sound continues to travelin air. If λa\lambda_a is wavelength in air, then
λa=vaυ=340106\lambda_a = \frac{v_a}{\upsilon} = \frac{340}{10^{6}} =3.4×10−4 m= 3.4 \times 10^{-4}\ \mathrm{m}
(b) The transmitted sound : The transmitted ultrasonic sound travels in water. If λw\lambda_w is wavelength of ultrasonic sound in water, then
λw=vwυ=1,486106\lambda_w = \frac{v_w}{\upsilon} = \frac{1{,}486}{10^{6}} =1.486×10−3 m= 1.486 \times 10^{-3}\ \mathrm{m}
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