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-1.5 m, linear density ? 1.7 g/m, and the oscillator frequency f= 200 Hz. The amplitude of the motion at P is small enough for that point to be considered a node. A node also exists at Q (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 m3 kg (Give 0 if the mass cannot set up a standing wave)? Oscillator D /m (a) Number kg (b) Number Units Units No units v Solution a) f=2/L×?(mg/muo) m =4×L^2×f^2×muo/n^2×g = 4×1.5^2×200^2×0.0017/16×9.8 = 3.903 kg b) if mass = 3 kg is given corresponding n is =?(4×L^2×f^2×muo/mg) = ?(4×1.5^2×200^2×0.0017/3×9.8) =4.56 Which is not a integer,therefore the mass cant setup standing wave in the string .

1. 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-1.5 m, linear density ? 1.7
g/m, and the oscillator frequency f= 200 Hz. The amplitude of the motion at P is small enough
for that point to be considered a node. A node also exists at Q (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 m3 kg (Give 0 if the mass cannot set up a standing wave)? Oscillator D /m (a)
Number kg (b) Number Units Units No units v
Solution
a) f=2/L×?(mg/muo)
m =4×L^2×f^2×muo/n^2×g
= 4×1.5^2×200^2×0.0017/16×9.8
= 3.903 kg
b) if mass = 3 kg is given corresponding
n is =?(4×L^2×f^2×muo/mg)
= ?(4×1.5^2×200^2×0.0017/3×9.8)
=4.56
Which is not a integer,therefore the mass cant setup standing wave in the string