In Qunick's acoustic interferometer , it is found that the sound intensity has a minimum value of 100 units at one position of the sliding tube , and cocontinuously climbs to a maximum of 900 units at a second position 1.65 cm from the first . Find (a) the frequency of the sound emitted by the source and (b) the relative amplitudes of the two waves arriving at the detector. Velocity of sound in air= 340 m//s.

In Qunick's acoustic interferometer , it is found that the sound inten

1.	In Qunick's acoustic interferometer , it is found that the sound intensity has a minimum value of 100 units at one position of the sliding tube , and cocontinuously climbs to a maximum of 900 units at a second position 1.65 cm from the first . Find (a) the frequency of the sound emitted by the source and (b) the relative amplitudes of the two waves arriving at the detector. Velocity of sound in air= 340 m//s.
Answer» Solution :a. Let `d_(1)` be the length of the FIXED path and `d_(2)` be the length of other path that can be varied . Then for minimum SOUND ` d_(2) - d_(1)= ( N + 1) lambda`. When the adjustable tube is MOVED out by `x` , the length of the path becomes ` d_(2) + 2 x`. For the next maximum sound `( d_(2) + 2 x ) - d_(1) = ( n + (1)/( 2)) lambda + ( lambda)/(2) = n lambda+ lambda` Subtracting ` 2 x= ( lambda)/( 2) orx = ( lambda)/( 4)` Here `x = 1.65 cm`. `:. lambda = 4 xx 1.65 = 6.6 cm = 6.6 xx 10^(-2) m` `C = n lambda or n = ( c)/( lambda) = (340)/( 6.6 xx 10^(-2)) = 5152 Hz` b. If `a and b`are the amplitudes of the waves , then minimum amplitude ` = a - b` and maximum amplitude ` = a + b` . ` :. (I_(MIN))/(I_(max)) = (( a - b)^(2))/(( a + b)^(2)) or (100)/(900) = (( a - b)^(2))/(( a + b)^(2))` or ` (a)/(b) = (2)/(1)`