In the arrangement shown below, an object can be hung from a string (with linear

Question

In the arrangement shown below, an object can be hung from a string (with linear mass density ? = 0.002 00 kg/m) that passes over a light pulley. The string is connected to a vibrator (of constant frequency f), and the length of the string between point P and the pulley is L = 2.50 m. When the mass m of the object is either 25.0 kg or 36.0 kg, standing waves are observed; no standing waves are observed with any mass between these values, however.

(a) What is the frequency of the vibrator? (Note: The greater the tension in the string, the smaller the number of nodes in the standing wave.) _____Hz

(b) What is the largest object mass for which standing waves could be observed?

_____kg

Explanation / Answer

a)Let n be the number of nodes in the standing wave resulting from the 36kg mass.

Then n + 1 is the number of nodes

for the standing wave resulting from the 25kg mass. for standing waves

= 2L/n and the frequency is f= v/

thus , f = n/2Lsqrt(F1/µ) and f = n+1/2Lsqrt(F2/µ)

n +1 / n = sqrt (F2/F1) = sqrt (36*g/25*g) = 6/5

n = 4 so f = 4/2*2.5 sqrt (25*9.8/0.002) = 280/s

b) V = f* = 280*2*2.5/4 =350 m/s

T =v^2*m/L = 350^2*36/2.5 = 1764000N

M = T/g = 180000kg

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