JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Waves & Sound

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In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is

336 ms^{- 1}

. The third resonance is observed when the air column has a length of

____

cm .

Answer: 104

Solution

For the first resonance:

ℓ_{1} + e = \frac{λ}{4}

Wavelength:

λ = \frac{v}{f} = \frac{336}{400} = 0.84

m = 84 cm

So

\frac{λ}{4} = 21

cm

End correction:

e = 21 - 20 = 1

cm

For the third resonance:

ℓ_{3} + e = \frac{5 λ}{4} = \frac{5 \times 84}{4} = 105

cm

Therefore:

ℓ_{3} = 105 - 1 = 104

cm

Answer: 104

JEE Main · 2022 · 29 Jun 2022 · Shift 2 · Integer answer

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