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Question

A boat is travelling in a river with a speed of 10m/s along the stream flowing with a speed 2m/s. From this boat, a sound transmitter is lowered into the river through a rigid support. The wavelength of the sound emitted from the transmitter inside the water is 14.45mm. Assume that attenuation of sound in water and air is negligible.
a. What will be the frequency detected by a receiver kept inside downstream?
b. The transmitter and the receiver are now pulled up into air. The air is blowing with a speed of 5m/s in the direction opposite the river stream. Determine the frequency of the sound detected by the receiver.
(Temperature of the air and water is 20C; density of river water is 103kg/m3 ; bulk modulus of the water is 2.088×109 Pa, gas constant R = 8.31J/mol – K; mean molecular mass of air is  for air is 28.8×103 kg/mol: cpcv for air is 1.4.)


  1. 100696 Hz, 103040 Hz
  2. 100545 Hz, 103646 Hz
  3. 100100 Hz, 103103 Hz
  4. 100425 Hz, 103954 Hz


Solution

The correct option is A 100696 Hz, 103040 Hz


a)  Speed of boat μ=10m/s
Speed of river stream w=2 m/s
Wavelength of sound wave inside water is 14.45 mm.
Speed of sound inside water is v=Bρ=[2.088×109103]
=2.088×103 m/s=1445 m/s
Frequency of wave inside water is
n=vλ=144514.45×103=105 Hz
In this case source and medium both are in motion.
Apparent frequency is given by
n=(v+w)(v+w)μn=(1445+2)(1445+2)10×105=14471437×105 Hz=1.00696×105 Hz=100696 Hz

b) Speed of sound air
v=γRTM=1.4×8.3×29328.8×103=344 m/s
Speed of air w=5m/s
n=(vw)(vw)μn=3445344510×105=339329×105 Hz=1.03040×105 Hz=103040 Hz
 

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