Choose the correct option. The tension in a piano wire is increased by 25%. Its frequency becomes ______ times the original frequency.

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The tension in a piano wire is increased by 25%. Its frequency becomes 1.12 times the original frequency. Explanation: Express the equation for frequency. f = v/lambda Here, f is frequency, v is velocity and λ is the wavelength. Express the equation for old velocity for the stretched string. v = sqrt(T/m) Here, T is old Tension and m is the mass density. Express the equation for the new velocity for the stretched string. v_0 = sqrt(T_0/m) ......(1) Here, T0 is old Tension and m is the mass density. Tension is increased by 25%. So express the equation for new tension. T0 = 1.25T, Here T0 is new tension and T is old tension. Substitute 1.25 T for T0 in the equation in (1). v_0 = sqrt((1.25T)/m) = sqrt(1.25) xx sqrt(T/m) = 1.118 xx sqrt(T/m) Substitute v for sqrt(T/m) to obtain new velocity. v_0 = 1.118 xx v = 1.12 v Therefore, the frequency becomes 1.12 times the original frequency.

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