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A 12.0 kg object hangs in equilibrium from a string with a total length of 5.00 m and a linear mass density =0.0010kg/m. The string is wrapped around two light , frictionless pulleys that are separated by a distance of d=2.0 m

a) determine the tension in the string

b) at what frequency must the string between the pulleys vibrate in order to form a standing wave with 3 antinodes?
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standing waves :

a)   The tension in the string is F = m g
given that m = 12-kg
acceleratiojdue to gravity g = 9.8 m / s2
so tension = 117.6 N

b)   given that seperation of pulleys d = l = 2.0 m
we know that  and
where v is velocity of the tansverse wave in the string
? is linear density
n is frequency of the string
l is the length of the string between the pulleys
as the string is vibrating with three loops its length is
using the above, on solving we can get the frequency of the stringas
n = 257.196Hz

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