In an experiment to measure the speed of sound by a resonating air...

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

500 H z

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 c m a n d 83.9 c m

. Which of the following statements is (are) true?

The speed of sound determined from this experiment is

332 m s^{- 1}

The end correction in this experiment is

0.9 c m

The wavelength of the sound wave is

66.4 c m

The resonance at

50.7 c m

corresponds to the fundamental harmonic

Solution:

Let

n_{1}

harmonic is corresponding to

50.7 c m a n d n_{2}

harmonic is corresponding

83.9 c m

. since both one consecutive harmonics.

∴

There difference

= \frac{λ}{2}

∴ \frac{λ}{2} = (83.9 - 50.7) c m

\frac{λ}{2} = 33.2 c m

λ = 66.4 c m

∴ \frac{λ}{4} = 16.6 c m

length corresponding to fundamental mode must be close to

\frac{λ}{4} a n d 50.7 c m

must be an odd multiple of this length

16.6 \times 3 = 49.8 c m

. therefore

50.7 i s 3^{r d}

harmonic
If end correction is e, then

e + 50.7 = \frac{3 λ}{4}

e = 49.8 - 50.7 = 0.9 c m

Speed of sound,

c = f λ

∴ v = 500 \times 66.4 c m / s e c = 332.000 m / s e c

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In an experiment to measure the speed of sound by a resonating air...

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In an experiment to measure the speed of sound by a resonating air...

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