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If the tension in a stretched string fixed at both ends is increased by $21 %$ , the fundamental frequency is found to be changed by $15 H z$ . Then, the

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original frequency is $150 H z$

velocity of propagation of the transverse wave along the string increases by $5 %$

velocity of propagation of the transverse wave along the string increases by $10 %$ .

fundamental wavelength on the string does not change

answer is A, C, D.

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Detailed Solution

$f = \sqrt{T}$

$\frac{f_{2}}{f_{1}} = \sqrt{\frac{T_{2}}{T_{1}}}$

$\frac{f_{1} + 15}{f_{1}} = \sqrt{\frac{121 T_{1}}{T_{1}}}$

$= 1.1$

Solving we get, $f_{1} = 150 H z$

$v = \sqrt{T}$

$\frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}}$

$v_{2} = (\sqrt{\frac{1.21 T_{1}}{T 1}}) v_{1}$

$= 1.1 v_{1}$

Hence, increase in v 10%

$\frac{λ}{2} = l$

Fundamental wavelength $= 2 l$ is unchanged.

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