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Question : 27 of 27
Marks: +1, -0
A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly towards a flat wall surface, the bat is moving at 0.03 times the speed of the sound in air. What frequency does the bat hear reflected off the wall?
Solution:  
Here, u=40 kHzu = 40\,\text{kHz},
speed of sound in air, v=340 m s−1v = 340\,\text{m s}^{-1}
∴ v′=v' = speed of bat
=0.03×v= 0.03 \times v =0.03×340=10.20 m s−1= 0.03 \times 340 = 10.20\,\text{m s}^{-1}
The bat moving towards wall acts as a moving source and for the sound waves reflected from the wall, it acts as a moving observer. Thus the source and observer are approaching each other with same speed.
i.e. vs=v0=v′=10.2 m s−1v_s = v_0 = v' = 10.2\,\text{m s}^{-1}
Thus apparent frequency of the reflected sound waves heard by the bat is given by
ν′=v+v0v−vs×ν=340+10.2340−10.2×40 kHz\nu' = \frac{v+v_0}{v-v_s} \times \nu = \frac{340+10.2}{340-10.2} \times 40\,\text{kHz}
=350.2329.8×40=42.47 kHz= \frac{350.2}{329.8} \times 40 = 42.47\,\text{kHz}
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