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Question: A resonating air column shows resonance with a tuning fork of frequency 256 Hz at column lengths 33....

A resonating air column shows resonance with a tuning fork of frequency 256 Hz at column lengths 33.4 cm and 101.8 cm. The speed of sound in air is

A

300 m s–1

B

250 m s–1

C

390 m s–1

D

350 m s–1

Answer

350 m s–1

Explanation

Solution

End correction =L2−3L12= \frac{L_{2} - 3L_{1}}{2}

=101.8−3×33.42= \frac{101.8 - 3 \times 33.4}{2}

=1.62=0.8cm= \frac{1.6}{2} = 0.8cm

Speed of sound

v=2υ(L2−L1)v = 2\upsilon(L_{2} - L_{1})

=2×256×(1.018−0.334)= 2 \times 256 \times (1.018 - 0.334)

=2×256×0.684=350.2ms−1= 2 \times 256 \times 0.684 = 350.2ms^{- 1}