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. (a) `5 grams`
B. (b) `10 grams`
C. ( c ) `20 grams`
D. (d) `40 grams`

Answer

B

Explanation

(b) Frequency of `2nd` harmonic of string = Fundamental frequency produced in the pipe

:. `2 xx [(1)/(2l_(1))sqrt((T)/(mu))] = (v)/(4l_(2)`
:. `(1)/(0.5)sqrt((50)/(mu)) = (320)/(4 xx 0.8)`
:. `mu = 0.02 kgm_(1)`
`The mass of the string = mul_(1)`
`= 0.02 xx 0.5kg = 10g`