Waves

JEE Main level, single correct, medium

105 of 142

Question 105 of 142

A tuning fork vibrates with frequency 256 Hz256 \mathrm{~Hz} and gives one best per second with the third normal mode of vibration of an open pipe. What is the length of the pipe? (Speed of sound of air is 340 ms−1340 \mathrm{~ms}^{-1} )

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Answer: (D) 200 cm200 \mathrm{~cm}

According to question, tuning fork gives 1 beat/second with (N) 3rd 3^{\text {rd }} normal mode. Therefore, organ pipe will have frequency (256±1)Hz(256 \pm 1) \mathrm{Hz}. In open organ pipe, frequency n=NV2ℓ\mathrm{n}=\frac{\mathrm{NV}}{2 \ell}
or, 255=3×3402×ℓ⇒ℓ=2 m=200 cm255=\frac{3 \times 340}{2 \times \ell} \Rightarrow \ell=2 \mathrm{~m}=200 \mathrm{~cm}

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