In the figure, a string, tied to a sinusoidal oscillator at P and running over a
ID: 1606451 • Letter: I
Question
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 = 1.4 m, near density mu = 0.8 g/m, and the oscillator frequency f = 140 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 m = 3 kg (Give 0 if the mass cannot set up a standing wave)?Explanation / Answer
Given that L=1.4m
=0.8g/m=0.0008kg/m
f=140HZ
a)
f=(nv/2)/L
where V=sqrt(mg/)
given n=4 (fourth harmonic)
f=[((nxsqrt(mg/))/2]/L
2fL/n=sqrt(mg/)
m=((2fL/n)2 x)/g
=(((2x140x1.4)/4)2 x0.0008)/9.8
m=0.784 kg
b)
here given m=3kg
string tension T=mg
T=3x9.8=29.4 N
V=sqrt(mg/)
=(29.4/0.0008)
V=191.7m/s
=v/f
=191.7/140
=1.37m