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2.
Two students want to use a 12-meter rope to create standing waves. They first measure the speed at
which a single wave pulse moves from one end of the rope to another and find that it is 36 m/s. This
information can be used to determine the frequency at which they must vibrate the rope to create
each harmonic. Follow the steps below to calculate these frequencies.
a.
Draw the standing wave patterns for the first six harmonics.
b.
Determine the wavelength for each harmonic on the 12-meter rope. Record the values in the table
below.
c.
24.2
Use the equation for wave speed (v = f ) to calculate each frequency.
Harmonic
1
2
3
4
5
6
Speed (m/s)
Wavelength
(m)
Frequency
(Hz)
36
36
36
36
36
36
d.
What happens to the frequency as the wavelength increases?
e.
Suppose the students cut the rope in half. The speed of the wave on the rope only depends on the
material from which the rope is made and its tension, so it will not change. Determine the wavelength
and frequency for each harmonic on the 6-meter rope.
Harmonic
1
2
3
4
5
6
f.
Speed (m/s)
Wavelength
(m)
Frequency
(Hz)
36
36
36
36
36
36
What effect did using a shorter rope have on the wavelength and frequency?