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A string 25 cm long and having a mass of 2.5 gm is under tension. A pipe closed at one end is 40 cm long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental frequency, 8 beats per second are heard. It is observed that decreasing the tension in the string decreases beat frequency. If the speed of sound in air is 320 m/s, find the tension in the string.

A string 25 cm long and having a mass of 2.5 gm is under tension. A pipe closed at one end is 40 cm long. When the string is set vibrating in its first overtone and the air in the pipe in its fundamental frequency, 8 beats per second are heard. It is observed that decreasing the tension in the string decreases beat frequency. If the speed of sound in air is 320 m/s, find the tension in the string.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Hello Student,
Please find the answer to your question
236-1502_123.png
Mass of string unit length = 2.5 x 10-3/0.25 = 0.01 kg/m
∴ Frequency, vs = 1/ℷ √T/m = 1/0.25 √T/0.01 . . . . . . . . . . . . . . . . . . . (i)
Fundamental frequency
∴ ℷ/4 = 0.4 ⇒ ℷ = 1.6 m
∴ vT = c/ℷT = 320/1.6 = 200 Hz . . . . . . . . . . . . . . . . . . . (ii)
Given that 8 beats/ seconds are heard. The beat frequency decreases with the decreasing tension. This means that beat frequency decreases with decreasing vs So beat frequency is given by the expression.
v = vs - vT
∴ 8 = 1/0.25 √T/0.01 – 200 ⇒ T = 27.04 N

Thanks
Aditi Chauhan
askIITians Faculty

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