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 receiver

200698

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100698

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300698

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400698

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Solution

The correct option is A $100698$ Hz
Velocity of sound in still air $(V_{s a}) = (γ R T / M)^{1 / 2} = 344$ m/s.
$f^{'} = f (V_{s a} - V_{a}) / (V_{s a} - V_{a} - V_{b}) = 100698$ Hz. Here $v_{a} =$ velocity of air.

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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 $20^{\circ} C$ ; density of river water is $10^{3} k g / m^{3}$ ; bulk modulus of the water is $2.088 \times 10^{9}$ Pa, gas constant R = 8.31J/mol – K; mean molecular mass of air is for air is $28.8 \times 10^{- 3} k g / m o l : \frac{c_{p}}{c_{v}}$ for air is 1.4.)