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

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`