Waves

JEE Main level, single correct, medium

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Question 71 of 142

A string 2.0m2.0m long and fixed at its ends is driven by a 240Hz240Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is

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Answer: (B) 320ms−1,80Hz320 {m s}^{-1}, 80 Hz

For a string fixed at both the ends,
f=n2Lvf=\dfrac{n}{2L}v
For third harmonic, 240=32(2)v240=\dfrac{3}{2(2)}v
⇒v=240×43\Rightarrow v=\dfrac{240\times 4}{3}
=320ms−1=320 m{s}^{-1}
Fundamental frequency f0=12Lv{f}_{0}=\dfrac{1}{2L}v
=14×320=80Hz=\dfrac{1}{4}\times 320 = 80 Hz

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