In the arrangement shown in the figure below, an object of mass m-2.00 kg hangs

Question

In the arrangement shown in the figure below, an object of mass m-2.00 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L-2.00 m. (Ignore the mass of the vertical section of the cord.) Vibrator (a) When the vibrator is set to a frequency of 172 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) wll result if m is changed to 4.50 kg? (Enter 0 if no loops form.) (c) How many loops (if any) will result if m is changed to 14.0 kg? (Enter O if no loops form.)

Explanation / Answer

there are 3 wavelengths so

3 lambda = 2

lambda = 2/3 m

f = 172 Hz

v = f lambda = 114.667 m/s

and v = sqrt[ T / mu ]

(114.6667^2) = (2 x 9.8) / mu

mu = 1.49 x 10^-3 kg/m .......Ans

(B) v = sqrt[ 4.50 x 9.8 / mu ] = 172 m/s

lambda = 1 m

so 2 wavelength -> 4 loops ....Ans

(C) v =sqrt(14 x 9.8 / mu) = 303 m/s

lambda = v/f = 1.75 m

Ans: No loops

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