First slide

Experiments to find speed of sound

Question

A tuning fork with frequency 800 Hz produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Successive resonance are observed at lengths 9.75 cm, 31.25 cm and 52.75 cm. The speed of sound in air is,

Moderate

A

172 m/s
B

500 m/s
C

156 m/s
D

344 m/s

Solution

$I_{1} = 9.75 cm I_{2} = 31.25 cm I_{3} = 52.75 cm e = end correction \frac{λ}{4} + e = 9.75 cm . . . (i) \frac{3 λ}{4} + e = 31.25 cm \dots (ii) \frac{3 λ}{4} - \frac{λ}{4} = 31.25 - 9.75 \frac{λ}{2} = 21.5 λ = 43 cm \begin{array}{l} v = λ \times f \\ v = 43 \times 800 \\ v = 34400 \times 10^{- 2} \end{array} v = 344 m / s$

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