A source of sonic oscillation with frequency `n_0=600Hz` moves away and at right angles to a wall with velocity `u=30(m)/(s)`. A stationary reciever is located on the line of source in succession wall`rarr`source`rarr`receiver. If velocity of osund propagation is `v=330(m)/(s)`, then
Q. The wavelength of reflected waves received by the receiver is

Options

A. beats frequency recorded by the receiver is 110 Hz
B. wavelengths of direct and reflected waves received by the receiver are 50 and 60 cm respectively
C. if receiver stands in between wall and source, beats recorded by the receiver is 0
D. if receiver stands between wall and source, then wavelengths of direct and reflected waves are 60 cm each

Answer

A, B, C, D

Explanation

(A) Beats will be recorded by observer because of two sound waves one direct from source and second which comes after reflection from the wall reaching him.
`f_("direct")=600((330+0)/(330-(+30)))=660Hz`
`f_("reflected")=f_("incident on wall")=600[(330+0)/(330-(-30))]=550Hz`
`therefore`Beat frequency
`f_(beat)=f_("direct")-f_("reflected")=660-550=110Hz`
(B) `lamda_("direct")=(V)/(f_("direct"))=(330)/(660)=0.5m=50cm`
`lamda_("reflected")=(v)/(f_("reflected"))=(330)/(550)=0.6m=60cm`.
(C) When receiver stands in between wall and source,
`f_("direct")=f_("reflected")`
`therfore f_(beat)=0`.
(D) When receiver stands in between wall and source,
`lamda_(direct)=lamda_("reflected")=(v)/(f_("direct"))=(v)/(f_("reflected"))=(330)/(550)=0.6m=60m`