A boat is travelling in a driver in river with a speed `10 m//s` along the stream flowing with a speed `2m//s`. From this, boat, a sounjd transmitter is lowered into the river through a right support. The wavelength of the sound emitted from the transmitter inside the water is `14.45 mm`. Assume that attention of sound in water and air is negligible.
(a) What will be frequency detected by receiver kept inside 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 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^(6) 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`).

Answer

(i) `100696 Hz
(ii) `1030338 Hz`

Explanation

Velocity of sound in water is
`V_(w)=sqrt((beta)/(rho))=sqrt((2.088xx10^(9))/(10^(3)))=1445m//s`
Frequency of sound in water will be
`f_(0)=(V_(w))/(lamda_(w))=(1445)/(14.45xx10^(-3))HzrArrf_(0)=10^(5)Hz`
(i) Frequency of sound detected by receiver (observer at rest would be).

`f_(1)=f_(0)((V_(w)+V_(tau))/(V_(w)+V_(tau)-V_(s)))=(10^(5))((1445+2)/(1445+2-10))Hz`
`f_(1)=1.0069xx10^(5)Hz`
(ii) Velocity of sound in air is
`V_(a)=sqrt((gammaRT)/(M))=sqrt(((1.4)(8.31)(20+273))/(28.8xx10^(-3)))=344m//s`
`:.` Frequency does not depend on the medium
Therefore, frequency in air is also `f_(0) = 10^(5) Hz`
`f_(0) = 10^(5) Hz`
`:.` frequency of sound detected by receiver (observer) in air would be
`f_(2)=f_(0)((V_(a)-w)/(V_(a)-w-V_(s)))=10^(6)[(344-5)/(344-5-10)]Hz`
`f_(2)=1.0304 xx10^(5)Hz`.