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 te

Step-by-step solution

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