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In a Kundt's tube experiment, a metallic rod of length 1 m is clamped at a point 25 cm from one end. The distance between successive heaps of powder in the tube is observed to be 50 cm, and the speed of sound in air is 330 m/s. Select the correct statement(s):

1. The frequency at which the tube oscillates is 1320 Hz
2. The frequency at which the tube oscillates is 330 Hz
3. The speed of the wave in the metallic rod is 330 m/s
4. The speed of the wave in the metallic rod is 1320 m/s

Correct answer: The frequency at which the tube oscillates is 330 Hz

Solution

The distance between consecutive powder heaps in Kundt's tube is lambda/2 for air, so lambda_air = 2 * 0.50 m = 1.00 m. The oscillation frequency f = v_air / lambda_air = 330/1 = 330 Hz. The rod clamped 25 cm from one end means the clamp is at a node; the rod length from clamp to far end is 75 cm and from clamp to near end is 25 cm, making the vibrating half-length 50 cm and full rod at a half-wavelength only if both ends are antinodes. Full analysis gives lambda_rod = 2L_rod for fundamental with clamp at center, but here clamp is at 1/4 point making lambda_rod/4 = 25 cm => lambda_rod = 100 cm = 1 m; v_rod = f * lambda_rod = 330 * 4 = 1320 m/s, not 330 m/s.

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