Question

If the tension in a stretched string fixed at both ends is increased by 21% the fundamental frequency is found to change by 15 Hz. Then the

• A. original frequency is 150 Hz
• B. velocity of propagation of the transverse wave along the string increases by 5%
• C. velocity of propagation of the transverse wave along the string increase by 10%
• D. fundamental wavelength on the string does not change

Answer 1

Answer: (A), (C), (D)

The correct options are
A original frequency is 150 Hz
C velocity of propagation of the transverse wave along the string increase by 10%
D fundamental wavelength on the string does not change

Speed of wave in the string is$v=\sqrt{\frac{T}{u}}$ where T=tension and u = mass per length

So,

fundamental frequency$f=\frac{n}{2L}\sqrt{\frac{T}{\mu }}$

where n is the number of harmonics.Number of overtones = (n-1)

Number of nodes = n+1

Number of antinodes = n

fundamental frequency= f=$\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

Note fundamental wavelength does not change as Length of the string does not change.

Here, T and f varies, new T=1.21T and new f=f +15

so, f+15=1.1f

This gives f=150Hz

so, new velocity=1.1v, which means velocity increases by 10%.