In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500…

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?
  1. The speed of sound determined from this experiment is 332 ms-1
  2. The end correction in this experiment is 0.9 cm
  3. The wavelength of the sound wave is 66.4cm
  4. The resonance at 50.7cm corresponds to the fundamental harmonic

Solution

Let n1 harmonic is corresponding to 50.7 cm and  n2 harmonic is corresponding 83.9 cm . since both one consecutive harmonics.
∴  There difference =λ2
∴ λ2=83.9-50.7cm
λ2=33.2 cm
λ=66.4 cm
∴ λ4=16.6cm
length corresponding to fundamental mode must be close to λ4 and 50.7 cm must be an odd multiple of this length 16.6 × 3 = 49.8 cm . therefore  50.7 is 3rd harmonic
If end correction is e, then
e+50.7=3λ4
e=49.8-50.7=0.9cm
Speed of sound, c=fλ
∴  v=500×66.4cm/sec=332.000m/sec

Asked in: JEE Advanced 2018 (Paper 2)

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