Question

In the arrangement shown in the figure below, an object of mass m =4.00 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.)

(a) When the vibrator is set to a frequency of 166 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 36.0 kg? (Enter 0 if no loops form.)


(c) How many loops (if any) will result if m is changed to 10.0 kg? (Enter 0 if no loops form.)

Examine how changing the mass affects the wave speed and wavelength and how that affects the number of loops. Should your answer be an integer?

Answer 1

Answer 2

5

Answer 3

Here we have n = 6 so f6 = 166 = 6*v/2L but v = sqrt(T/?)

And T = m*g

so 166 = 6*sqrt(T/?)/2L

So ? = (6/166)^2*T/4L^2 = (6/166)^2*m*g/(4L^2) = (6/166)^2*4.0*9.8/(4*2^2) =0.0032kg/m

b) Now f= 166 = n*sqrt(T/?)/(2L)

So n = 166*2*L/sqrt(m*g/?) = 166*2*2.0m/sqrt(36.0*9.8/0.0032) = 2.5 = ~3

c) Now f= 166 = n*sqrt(T/?)/(2L)

So n = 166*2*L/sqrt(m*g/?) = 166*2*2.0m/sqrt(10.0*9.8/0.0032) = 3.8 = ~ 4