A 25 cm long string is fixed at both ends. It has a mass of 2 . 5 g and vibrates in its first overtone under tension. Also given is a closed pipe which is 30 cm long which vibrates in its fundamental frequency. When both of these are sounded simultaneously, 8 beats per second are heard. It is also observed that decreasing the tension in the string also decreases the beat frequency. What is the tension (in N ) in the string? [Given, speed of sound in air is 360 ms - 1 ]

Question

A 25 cm long string is fixed at both ends. It has a mass of 2 . 5 g and vibrates in its first overtone under tension. Also given is a closed pipe which is 30 cm long which vibrates in its fundamental frequency. When both of these are sounded simultaneously, 8 beats per second are heard. It is also observed that decreasing the tension in the string also decreases the beat frequency. What is the tension (in N ) in the string? [Given, speed of sound in air is 360 ms - 1 ],

MARKS App · Accepted Answer

μ = 2 . 5 25 = 0 . 1 g / cm = 10 - 2 kg / m 1 st overtone, λ s = 25 cm = 0 . 25 m ⇒ f s = 1 λ s T μ Pipe in fundamental frequency, λ p 4 = 0 . 3 λ p = 1 . 2 m ⇒ f p = v s λ p = 360 1 . 2 = 300 Hz ∵ By decreasing the tension, beat frequency is decreased. ∴ f s > f p ⇒ f s - f p = 8 ⇒ 1 0 . 25 T 10 - 2 - 360 1 . 2 = 8 ⇒ 10 × 100 25 T - 300 = 8 ⇒ T = 308 × 25 1000 ⇒ T = 59 . 29 N

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