Waves

JEE Main level, numerical answer, medium

132 of 142

Question 132 of 142

The fundamental frequency of vibration of a string between two rigid support is 50Hz50Hz. The mass of the string is 18g18g and its linear mass density is 20gm−120g{m}^{-1}. The speed of the transverse waves so produced in the string is _______ ms–1m{s}^{–1}.

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Answer: 90

The fundamental frequency is f=50Hzf=50Hz.
The length of the string is l=λ2l=\dfrac{\lambda }{2}
Linear mass density is μ=ml=20gm−1\mu =\dfrac{m}{l}=20g{m}^{-1}
Using v=fλv=f\lambda
v2l=50\dfrac{v}{2l}=50
⇒v=100×l=100×1820=90ms−1\Rightarrow v=100\times l=\dfrac{100\times 18}{20}=90m{s}^{-1}

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