In the arrangement shown below, an object ofmass m = 3.0 kg hangs from a cordaro

Question

In the arrangement shown below, an object ofmass m = 3.0 kg hangs from a cordaround a light pulley. The length of the cord betweenpointP and the pulley is L = 2.0m.
(a) When thevibrator is set to a frequency of 120 Hz, a standing wavewith six loops is formed. What must be the linear mass density ofthe cord? (b) How manyloops (if any) will result if m is changedto 108 kg? (c) How manyloops (if any) will result if m is changedto 4.32 kg?
(a) When thevibrator is set to a frequency of 120 Hz, a standing wavewith six loops is formed. What must be the linear mass density ofthe cord? (b) How manyloops (if any) will result if m is changedto 108 kg? (c) How manyloops (if any) will result if m is changedto 4.32 kg?

Explanation / Answer

frequancy of the waves on stringkept under tension             f = v /2L            v = (T/)            f = (T/) / 2L         T= tension onthe string = mg         m = masshanged          =linear density of string          L =length of string . we know T , L and f , plugging givenvaleus in abv relaion we can solve for liear density. b) if the tension on the stringchanges number of loops = n = L /             = v /f      v =velocity canbe determined and f = v / 2L use abv relation and solve for n. c) fallow the same procedure asabv.

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