Chapter 16, Problem 058 In the figure, a string, tied to a sinusoidal oscillator

Question

Chapter 16, Problem 058 In the figure, a string, tied to a sinusoidal oscillator at p and running over a support at Q, is stretched by a block of mass m. Separation L = 1.0 m, linear density at Q = 0.8 g/m, and the oscillator frequency f= 130 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists (a) What mass m allows the oscillator to set up the fourth harmonic on the string? (b) What standing wave mode, if any, can be set up if m4 kg (Give 0 if the mass cannot set up a standing wave)? Oscillator P 2m (a) Number Units (b) Number Units

Explanation / Answer

a) mass m = 4 L2 f2 mu / n2 g

= (4 * 1.02 * 1302 * 0.8 * 10-3) / (42 * 9.8)

mass m = 0.345 kg

b)  m = 4 L2 f2 mu / n2 g

2 = (4 * 1.02 * 1302 * 0.8 * 10-3) / (n2 * 9.8)

n2 = (4 * 1.02 * 1302 * 0.8 * 10-3) / (2 * 9.8)

n = 1.66

As n is not integer so it cannot form standing waves = 0

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