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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

In a resonance column experiment, a tuning fork of frequency 400 Hz...

In a resonance column experiment, a tuning fork of frequency 400 Hz400 \text{ Hz} is utilized. The first resonance is noticed when the length of the air column is 20.0 cm20.0 \text{ cm}, while the second resonance occurs when the air column length is 62.0 cm62.0 \text{ cm}. Find the speed of sound in air.

Options

  1. A344 m s−1344 \text{ m s}^{-1}
  2. B320 m s−1320 \text{ m s}^{-1}
  3. C336 m s−1336 \text{ m s}^{-1}
  4. D352 m s−1352 \text{ m s}^{-1}

Correct answer

C. 336 m s−1336 \text{ m s}^{-1}

Step-by-step solution

Let L1L_1 and L2L_2 be the lengths of the air column for the first and second resonances respectively.

L1=20.0 cm=0.20 mL_1 = 20.0 \text{ cm} = 0.20 \text{ m}
L2=62.0 cm=0.62 mL_2 = 62.0 \text{ cm} = 0.62 \text{ m}
f=400 Hzf = 400 \text{ Hz}

The wavelength λ\lambda is given by:
λ=2(L2−L1)\lambda = 2(L_2 - L_1)

The speed of sound vv is:
v=fλ=2f(L2−L1)v = f\lambda = 2f(L_2 - L_1)

Substituting the given values:
v=2×400×(0.62−0.20)v = 2 \times 400 \times (0.62 - 0.20)
v=800×0.42=336 m s−1v = 800 \times 0.42 = 336 \text{ m s}^{-1}
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