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4. If y = 0.02 sin ((30m-1 )x

4. If y = 0.02 sin ((30m-1 )x

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4. Comparing the given equation with the following stsndard equation of wave displacement

Here, A is the amplitude, k is the wave number, omega is the angular velocity. On comparison we get

The velocity of the wave is given as

wave velocity is 13 m/s so option b is correct.

4. The formula for the frequency of the standing waves

L is the length of the string, v is the wave speed and n is an interger. For the third harmonic n=3 so the frequency of the third harmonic becomes

So option c is correct.

5. We need to find the speed v of the wave travelling on the string

T is the tension and mu is the linear mass density.

For second harmonic n=2, Putting all the values in Eq. (1) we get

Frequency of second harmonic is 200Hz so option b is correct.

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