Figure 7.88 shows a stretched string of length `L` and pipes of length `L , 2L , L//2 and L//2` in options (a) , (b), (c ) and (d) respectively . The string 's tension is adjusted until the speed of waves on the string equals the speed of sound waves in the air . The fundamental mode of oscillation is the set up on the string . In which pipe will the sound produced by the string cause resonance ?

Options

A.
B.
C.
D.

Answer

B

Explanation

Fundamental frequency of wire `(f_(wire)) = v//2l`
a . `f = (v)/( 4 l) , (3 v)/( 4 l) , ( 5 v)/( 4 l)`cannot match with `f_(wire)`
b. ` f = (v)/(2( 2 l)) , ( 2 v)/( 2 ( 2 l)) , ( 3 v)/( 2 ( 2l))` its second harmonic `( 2 v)/( 2 ( 2l))` matches with `f_(wire)`. c. `f = (v)/(2 (l//2)) , ( 2 v)/( 2 (l//2))` cannot match with `f_(wire)`
`f = (v)/( 4 (l//2)) ,( 3 v)/( 4 ( l//2)),.... ` cannot match with `f_(wire)`