Two turning forks A and B are sounded together and 8 beats / sec are heated . A is in resonance with column of air 32 cm long in a pipe closed at one end and B is increased by one cm . Calculate frequency of fork ?

Two turning forks A and B are sounded together and 8 beats / sec  are heated .  A is in resonance with column of air 32 cm long in a pipe closed at one end and B is increased by one cm . Calculate frequency of fork ?

A ) fa = 264 Hz  and  fb = 256 Hz   ,       

B ) fa = 256 Hz  and  fb = 264 Hz   ,

C ) fa = 298 Hz  and  fb = 216 Hz   ,

D ) fa = 216 Hz  and  fb = 298 Hz   ,                    

Correct Answer : -   A ) fa = 264 Hz  and  fb = 256 Hz   ,     

Solution : -

Formula : -

To produce beats , frequency must be different .

fa – fb = n  ,    { f = frequency  ,  n = beats }

fa – fb = 8   . . . . . . . . . . . . . eq. 1

so , as given ;

λa = 32 cm = 0.32 m  ,  λb = 33 cm = 0.33 m  and   fa > fb .

And we have formula : -  v = f λ  and  f = v / λ  .

So  ,  

fa = v / ( 4 x 0.32 )  . . . . . . . . . . . eq. 2 ,

fb = v / ( 4 x 0.33 )  . . . . . . . . . . .  eq. 3 .

So put values of fa and fb in  eq. 1 ;

v / ( 4 x 0.32 )  -   v / ( 4 x 0.33 )  =  8  ,

v = 338  m / sec .

Now put value of v in eq . 2 and 3 .

fa = 338 / ( 4 x 0.32 ) .

fb = 338 / ( 4 x 0.33 ) .

So after solving we will have answers : -

fa = 264 Hz  and  fb = 256 Hz   ,    Answer .