In a resonance experiment, two air columns closed at one end have lengths 100 cm and 120 cm. Their fundamental frequencies produce 15 beats per second. The velocity of sound is:
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Question

In a resonance experiment, two air columns closed at one end have lengths 100 cm and 120 cm. Their fundamental frequencies produce 15 beats per second. The velocity of sound is:

G1 Physics · Accepted Answer

For a closed pipe in the fundamental mode, f = v/(4L). Thus the beat frequency is |f₁-f₂| = 15. Using L₁=1.0 m and L₂=1.2 m: 15 = v/4 |1/1.0 - 1/1.2|. Now, 1 - 1/1.2 = 1 - 5/6 = 1/6. Therefore, 15 = v/(24) ⇒ v = 360 m/s. Correct option: D.