JEE Advanced 2018 · Paper 2 · Physics Q6

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PhysicsMultiple correct+4 / -2Question 6 of 54

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?

The speed of sound determined from this experiment is

332\ \mathrm{m\,s^{-1}}

The end correction in this experiment is 0.9 cm

The wavelength of the sound wave is 66.4 cm

The resonance at 50.7 cm corresponds to the fundamental harmonic

Answer and worked solution

Official answer: A, B, C

Wavelength. Successive resonances differ by $\lambda/2$ :
$\frac\lambda2=83.9-50.7=33.2\text{ cm}\implies\lambda=66.4\text{ cm}.$
(C) is true.

Speed. $v=500\times0.664=332\ \mathrm{m\,s^{-1}}$ . (A) is true.

Which harmonic? $\lambda/4=16.6$ cm, so the fundamental would be heard near 16.6 cm. 50.7 cm is close to $3\lambda/4=49.8$ cm, the second resonance. (D) is false.

End correction. Matching $L+e=3\lambda/4$ gives $e=49.8-50.7=-0.9$ cm. Its size is 0.9 cm, but a physical end correction must be positive. That is why the official key accepts both ABC and AC.

Answer: (A), (C), with (B) also accepted (key: ABC or AC)

Topics:Speed of sound by resonance tube Organ pipes and resonance

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JEE Advanced 2018 · Paper 2, Physics question 6