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 throught a rigid support. The wavelength of the sound emitted from the transmitter inside the water is `14.45 mm` . Aassume that attenuation of sound in water and air is neglisible.
(a) What will be the frequency delected by a receiver kept inside the river downstream ?
(b) The transmitter and the reciver 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 delected by the reciver.
(Temperature of the air and water = `20^(@) C` , Density of river water = `10^(3) kg//m^(3)` , Bulk modulus of the water = `2.088 xx10 ^(9) Pa` , Gas constant, `R= 8.31 J//mol - K` , Mean molecular mass of air = `28.8xx 10 ^(-3) kg//mol` , `C_(p)//C_(V)` for air = `1.4`

Explanation

(a)Velocity of sound in still water `(V_(SW))=(B//rho)^(1//2)`=1445 m/s
`f=(V_(SW))//(lambda_W)=10^5` Hz, `f.=f(V_(SW)+V_W)//(V_(SW)+V_W-V_b)`
=100696 Hz
Here `V_W` = velocity of water stream ,`V_b` = velocity of boat
(b) Velocity of sound in still air `(V_(sa))=(gammaRT//M)^(1//2)` =344 m/s
`f.=f(V_(sa)-V_a)//(V_(sa)-V_a-V_b)`=100698 Hz . Here `V_a` = velocity of air