Question

A string fixed at both ends is 10 m long and has a mass of 0.23 kg. It is subjected to a tension of 120 N and set oscillating. (a) What is the speed of the waves on the string? (b) What is the longest possible wavelength for a standing wave? (c) Give the frequency of that wave.

Answer 1

Solution)

Given,

Length, l=10 m

Mass, m=0.23 kg

Tension, T=120 N

Linear density, Mu=0.23 kg/10 m

Part a)

We know, speed, v= sqrt(T/Mu)

On substituting values, we have

Speed, v=sqrt(120 N*10m/0.23 kg)= 72.23 m/s (Ans)

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Part b)

We know,

Longest possible wavelength, lambda occurs ar, n=1

So,

Lambda=2*length=2*10m=20 m (Ans)

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Part c)

We know,

Frequency, f= v/lambda= (72.23 m/s)/20m= 3.61 Hz (Ans)

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