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 leavel 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?

Options

A. The speed of sound determined from this experiment is `332ms^(-1)`
B. The end correction in this experiment is 0.9 cm
C. The wavelength of the sound wave is 66.5 cm
D. The resonance at 50.7 cm corresponds to the fundamental harmonic

Answer

A, B, C

Explanation

`500=(2n+1)(v)/(4(0.507+e))implies2000(0.507+e)=(2n+1)v`….(i)
`500=(2n+3)(v)/(4(0.839+e))implies 2000(0.839+e)=(2n+3)v` ….(ii)
(ii)-(i) 2000(0.839-0.507)=2v
`implies v=1000(0.332)=332 m//s ` (A is correct)
`lambda=v/f=332/500=66.4xx10^(-2)m=66.4 cm` (C is correct)
Neglecting end correction to find the mole for length 50.7 cm
`500=(2n+1)((332))/(4(0.507))implies 2n+3` (forst overtone) (D is correct)
For e:`500=(3(332))/(4(0.507+e))implies e=-0.009m=-0.9cm`
The avsolute value of end correction may be considered as 0.9)