A hollow pipe of length 0.8 m 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

Question

A hollow pipe of length 0.8 m 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

TestHub · Accepted Answer

2 ( 2 l 1 ​ v 1 ​ ​ ) = 4 l 2 ​ v 2 ​ ​ ∴ l 1 ​ T / μ ​ ​ = 4 l 2 ​ 320 ​ ( μ = mass per unit length of wire) or 0.5 50/ μ ​ ​ = 4 × 0.8 320 ​ Solving we get μ = 0.02 m kg ​ = 20 m g ​ ∴ Mass of string = ( 20 m g ​ ) ( 0.5 m ) = 10 g ∴ The correct option is (b).

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