Question

A pipe closed at one end has length 0.8 cm. 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 m/s, the mass of the string is ______.

Options

• 2 gram

• 8 gram

• 4 gram

• 10 gram

Answer 1

A pipe closed at one end has length 0.8 cm. 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 m/s, the mass of the string is 10 gram.

Explanation:

`2 [1/(2l_1) sqrt("T"/"m")] = "v"/(4l_2)`

`1/0.5 sqrt(50/"m") = 320/(4 xx 0.8)`

∴ m = 0.02 kg/m

∴ Total mass of the string = 0.02 × 0.5 kg = 10 gm