A boat is travelling in a river with a speed `10m//s` along with stream flowing 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 the river downstream?
(b) The transmitter and the receiver are now pulled up into air. the air is blowing with a speed `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 = `20^(@)C`, Density of river water `= 10^(3) kg//m^(3)`,
Bulk modulus of the water `= 2.088 xx 10^(9)`Pa, gas constant `R = 8.31 J//mol-K`,
Mean molecular mass of air `= 28.8 xx 10^(-3) kg//mol`, `C_(P)//C_(V)` for air `= 1.4`)

Explanation

Speed of boat`u=10(m)/(s)`
Speed of river stream `w=2(m)/(s)`
Wavelength of sound wave inside water is 14.45mm. Speed of sound inside water is
`v=sqrt((B)/(d))=sqrt({(2.088xx10^9)/(10^3)})`
`=sqrt(2.088)xx10^3(m)/(s)=1445(m)/(s)`
Frequency of wave inside water is
`n=(v)/(lamda)=(1445)/(14.45xx10^(-3))=10^3Hz`
In this case source and medium both are in motion
Apparent frequency is given by
`n'=((v+w))/((v+w)-u)n=((1445+2))/((1445+2)-10)xx10^5`
`=(1447)/(1437)xx10^5Hz=1.00696xx10^5Hz`