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A boat is travelling in a river with a speed 10 m/s along the stream flowing with a speed 2 m/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 14:45 mm. Assume that attenuation of sound in water and air is negligible. (a) What will be the frequency detected by a receiver kept inside the river downstream? (b) The transmitter and the receiver are now pulled up into air. The air is blowing with a speed 5 m/s in the direction opposite the river stream. Determine the frequency of the sound detected by the air receiver. (Temperature of the air and water = 20° C; Density of river water = 10 3 kg/m 3 ; Bulks modulus of the water = 2.088 x 10 9 Pa ; Gas constant R = 8.31 J/mol – K ; Mean molecular mass of air = 28.8 x 10 -3 kg/mol ; C p C v for air = 1.4)

A boat is travelling in a river with a speed 10 m/s along the stream flowing with a speed 2 m/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 14:45 mm. Assume that attenuation of sound in water and air is negligible.
(a) What will be the frequency detected by a receiver kept inside the river downstream?
(b)  The transmitter and the receiver are now pulled up into air. The air is blowing with a speed 5 m/s in the direction opposite the river stream. Determine the frequency of the sound detected by the air receiver.
(Temperature of the air and water = 20° C; Density of river water = 103 kg/m3 ; Bulks modulus of the water = 2.088 x 109 Pa ; Gas constant R = 8.31 J/mol – K ; Mean molecular mass of air = 28.8 x 10-3 kg/mol ; Cp Cv for air = 1.4)

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Hello Student,
Please find the answer to your question
KEY CONCEPT : The question is based on Doppler’s effect where the medium through which the sound is travelling is also in motion.
By Doppler’s formula
v’ = v[ c + vm± v0/c + vm± vs] . . . . . . . . . . . . . . . . . (i)
NOTE : Sign convention for Vm­is as follows : If medium is moving from s to O then +ve and vice versa. Similarly v0and vsare positive if these are directed from S to O and vice versa.
(a) Situation 1.
236-1844_6.png
Velocity of sound in water c = √B/p = √2.088 x 109/103
c = 1445 m/s; vm = + 2m/s’ v0 = 0; vs = 10 m/s
∴ v’ = v [1445 + 2 – 0/1445 + 2 – 10] = v [1.007]
Now v = c ℷ = 1445/14.45 x 10-3 = 105 Hz
∴ v’ = 1.007 x 105 Hz
(b) Situation 2.
In air c = √y RT/M = 344 m/s
Applying formula (1)
v’ = v [344 – 5 – 0/344 – 5 – 10] = 1.03 x 105 Hz
236-1744_6.png

Thanks
Aditi Chauhan
askIITians Faculty

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