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

(i) `1.007xx10^(5) Hz` (ii) `1.03xx10^(5)HZ`
Situation-1
Speed of sound inside the water `=sqrt((B)/(rho))=sqrt((2.088xx10^(9))/(10^(3)))=1445 m//s`
The frquency sound inside the water `f=(v)/(lambda)=(1445)/(14.45xx10^(-3))=10^(5)Hz`
In this case the medium through which the soundis travelling is laso motion so we will use the relation ofDoppler's formula
Apparent frequency
`f'=f[((v+v_m)+v_0)/((v+v_m)-v_s)]`.....(i)
`v_m=2m//s,v_0=0,v_s=1=m//s`
The frequency detected bya receiver
`f'=10^(5)[(1445+2-0)/(1445+2-10)]`
Situation
Frequency of sound wave will be same as if does nochnge with change in medium in air `C=sqrt((gammaRT)/(M))=344 m//s`
Again apllying equation (i) `f'=10^(5)[(344-5-0)/(344-5-10)]=1.03xx10^(5) Hz