A sonometer wire of length l vibrates in fundamental mode when excited by a tuning fork of frequency 416. Hz. If the length is doubled keeping other things same, the string will ______.

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KollegeApply · Accepted Answer

vibrate with a frequency of 208 Hz According to the relation of the fundamental frequency of a string \nu = $\frac{1}{2}$l$\sqrt$(F/\mu) where l is the length of the string F is the tension μ is the linear mass density We know that ν1 = 416 Hz, l1 = l and l2 = 2l. v_1 \propto 1/l_1 v_1 l_1 = v_2 l_2 \left( 416 \right)l = v_2 \left( 2l \right) v_2 = 208 Hz

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