A boat is travelling in a river with a speed of 10 m/s along the stream flowing with a speed of 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 14.45 mm. Assume that attenuation of sound in water and air is negligible. What will be the frequency detected by a receiver kept inside downstream?

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`