A hollow pipe of length `0.8m` is closed at one end. At its open end a `0.5 m` long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is `50 N` and the speed of sound is `320 ms^(-1)`, the mass of the string is

Options

A. 5 g
B. 10 g
C. 20 g
D. 40 g

Answer

B

Explanation

`(v_(s))/(4 L_(P)) = (2)/(2l_(S)) sqrt((T)/(mu)) rArr (320)/(4 xx 0.8) = (1)/(0.5) sqrt((50)/(mu))`
`rArr mu = 1//50`
Mass of string,
`m = mu l_(S) = (1)/(50) xx 0.5 = 0.01 kg = 10 g`.