Gce Model Questions Vol1 2025 Physics Question 10

A string of length L = 1.20 m is fixed at both ends. Its linear mass density is μ = 2.5×10⁻² kg m⁻¹. Initially the string is under a tension T₁ = 80 N, giving a fundamental frequency f₁. The tension is then increased to T₂ = 120 N, producing a new fundamental frequency f₂. (a) Determine f₁ and f₂. (b) The string at tension T₁ is plucked to vibrate in its fundamental mode. At the same time, a second identical string (same L and μ) is driven by an electronic oscillator at its fundamental frequency when the tension is 100 N. Find the beat frequency that would be heard. (c) When the string is kept at tension T₂, the amplitude of the standing wave decays with time according to A(t) = A₀ e^{‑t/τ}. If after 5.0 s the total mechanical energy of the standing wave is half its initial value, determine the decay constant τ. (d) Using the results obtained, discuss qualitatively how increasing the tension of a string influences (i) the speed of transverse waves on the string and (ii) the pitch of the musical note produced.