A source of sound of frequency f is approaching towards a wall with speed upsilon_(s) . Speed of sorce is upsilon . Three obseruers O_(1) , O_(2) and O_(3) are at different locations as shows . Find the beat frequency as obserued by three different obseruers.

A source of sound of frequency f is approaching towards a wall with sp

1.	A source of sound of frequency f is approaching towards a wall with speed upsilon_(s) . Speed of sorce is upsilon . Three obseruers O_(1) , O_(2) and O_(3) are at different locations as shows . Find the beat frequency as obserued by three different obseruers.
Answer» Solution :For reflected sound we can take wall as a PLANE mirror. Observer `O_(1)S` is RECEDING from `O_(1)` and `S` ' i`((2upsilon_(s))/(upsilon- upsilon_(s))) f` approaching towards him. So, `f_(s')gtf_(s)` `f_(b) = f_(s') - f_(s)` = `f (upsilon/(upsilon - upsilon_(s)))- f(upsilon/(upsilon + upsilon_(s)))` = `((2 upsilon upsilon_(s))/(upsilon^(2) - upsilon_(s)^(2))) f` Observer `O_(2)``O_(2)` has no RELATIVE motion with `S` . Therefore, there will be no change in the frequency of direct sound from `S` . Further, `O_(2)` and `S` ' are approaching towards each other. Therefore, the frequency of reflected sound will increase. `f_(b) = f_(s') -f_(s)` = `f ((upsilon + upsilon_(02))/(upsilon - upsilon_(s))) - f` But `upsilon_(02) = upsilon_(s)` `:. f_(b) = f ((upsilon + upsilon_(s))/(upsilon - upsilon_(s))) - f` = `((2upsilon_(s))/(upsilon- upsilon_(s))) f` Observer `O_(3)S` and `s'` both approaching towards `O_(3)` . SO, both frequenceies will increase. But after the increease theyare equal . So, beat frequency will be zero. `f_(s) = f_(s')= f ((upsilon)/(upsilon - upsilon_(s)))` `:. f_(b) = f_(s) - f_(s') = 0`