A string of length ℓ fixed at one end and free at another end is vibrating in 5th harmonic. Maximum displacement of particle is A. Amplitude of oscillation of a particle at distance 10 ℓ from free e

Question

A string of length ℓ fixed at one end and free at another end is vibrating in 5th harmonic. Maximum displacement of particle is A. Amplitude of oscillation of a particle at distance 10 ℓ ​ from free end is α ​ A ​ , find value of α .

TestHub · Accepted Answer

Fixed-free string, 5th harmonic: 4 5 λ ​ = ℓ ⇒ λ = 5 4 ℓ ​ . Particle at ℓ /10 from the free end sits at x = 9 ℓ /10 from the fixed end: A x ​ = A ​ sin λ 2 π x ​ ​ = A sin 4 9 π ​ = 2 ​ A ​ . With amplitude A / α ​ : α = 2 .

Physics - Wave on String Question with Solution | TestHub

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