The drawing shows an arrangement in which a block (mass = 16.7 kg) is held in po

Question

The drawing shows an arrangement in which a block (mass = 16.7 kg) is held in position on a frictionless incline by a cord (length = 0.530 m). The mass per unit length of the cord is 1.03 x 10-2 kg/m so the mass of the cord is negligible compared to the mass of the block. The cord is being vibrated at a frequency of 185 Hz (vibration source not shown in the drawing). What is the maximum value of the angle ? in degrees at which a standing wave pattern exists on the cord?

Explanation / Answer

v = wavelength * f = L * f = 0.53*185 = 98.05 m/s ------------------------------------------------------------------------------------------------------------------------------------------------------------------- T = u v^2 = (1.03e-2) * 98.05*98.05 = 99.02216575 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- m g sin(t) = T ==> 16.7 * 9.8 * sin(t) = 99.02216575 ------------------------------------------------------------------------------------------------------------------------------------------------------------------- ===> angle = 37.2 degrees -------------------------------------------------------------------------------------------------------------------------------------------------------------------

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