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 gram
B. 10 gram
C. 20 gram
D. 40 gram

Answer

B

Explanation

The fundamental frequency of the pipe
` n = v/(4L) = 320/(4 xx 0.8) = 100` Hz
` :. ` For the string second harmonic = 100 Hz
`:. 100 = 2/(2L) sqrt(T/m) = 2/(2 xx 1/2) sqrt(50/m) = 2 sqrt(50/m) `
` 50 = sqrt(50/m) :. 50 xx 50 = 50/m :. m = 1/50 ` kg
` :. ` Mass of the string ` = m xx L `
` = 1/50 xx 1/2 = 1/100 kg ` ltrgt ` = 1/100 xx 1000 = 10 ` g