In the arrangement shown in the figure below, an object of mass m = 6.0 kg hangs

Question

In the arrangement shown in the figure below, an object of mass m = 6.0 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L = 2.0 m. (Ignore the mass of the vertical section of the cord.) (a) When the vibrator is set to a frequency of 160 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord? kg/m (b) How many loops (if any) will result if m is changed to 13.5 kg? (Enter 0 if no loops form.) loops (c) How many loops (if any) will result if m is changed to 10 kg? (Enter 0 if no loops form.) loops

Explanation / Answer

Here we have n = 6 so

f6 = 160 = 6*v/2L but v = sqrt(T/?)

And T = m*g

so 160 = 6*sqrt(m*g/?)/2L

So ? = ((6/160)^2)*6*9.8/(4*(2^2)) = 5.16x10^-3kg/m

b) Now f= 160 = n*sqrt(T/?)/(2L)

So n = 160*2*2/sqrt(m*g/?) = 160*2*2/sqrt(13.5*9.8/5.16x10^-3) = 4

c) Now f= 160 = n*sqrt(T/?)/(2L)

So n = 160*2*L/sqrt(m*g/?) = 160*2*2/sqrt(10*9.8/5.16x10^-3) = 4.64 , so n = 0

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