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Question: A bat emits ultrasonic sound of frequency 100 kHz in air. If this sound meets a water surface, the w...

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 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

3.4 mm, 15 mm

Explanation

Solution

Here, υ=100kHz=100×103Hz\upsilon = 100kHz = 100 \times 10^{3}Hz

=105Hz=105s−1= 10^{5}Hz = 10^{5}s^{- 1}

va=340ms−1,vw=1500ms−1v_{a} = 340ms^{- 1},v_{w} = 1500ms^{- 1}

Frequency of both the reflected and transmitted sound remains unchanged.

Wavelength of reflected sound.

λa=vaυ=340ms−1105s−1=34×10−4m\lambda_{a} = \frac{v_{a}}{\upsilon} = \frac{340ms^{- 1}}{10^{5}s^{- 1}} = 34 \times 10^{- 4}m

=3.4×10−3m=3.4mm= 3.4 \times 10^{- 3}m = 3.4mm

Wavelength of transmitted sound,

λw=vwυ=1500ms−1105s−1=15×10−3m=15mm\lambda_{w} = \frac{v_{w}}{\upsilon} = \frac{1500ms^{- 1}}{10^{5}s^{- 1}} = 15 \times 10^{- 3}m = 15mm