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PHY138Y |
Waves
Assignment 3 |
Prof. Jason Harlow |
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Physics Department |
Due |
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Please complete the following problems on separate
paper. Show all your work legibly, and
draw a box around the final numerical answer where applicable. Use one staple in the upper left-hand corner
to connect multiple pages, and slip the entire assignment in the drop-box for
your Tutorial Section at the bottom of the stairs of
Supplemental Problem:
A standing wave is set up on
a single string, as shown above. The two
fixed ends are attached to walls 73 cm apart.
The string is represented at several times.
a) What is the wavelength of
the traveling waves on the string which make up this standing wave?
b) If waves on the string
travel at a speed of 15 m/s, what is the frequency of the standing wave that is
shown?
c) What mode of vibration is
shown?
From the Textbook:
14.4, 14.29, 14.36 (part a
only), 24.32
Some suggested problems from the Textbook (not to be
turned in):
Question 11 on page 495
Problems 14.5, 14.11, 14.21,
14.25, 14.28, 14.35
Question 13 on page 925
Problem 24.35
Some PHY138Y Laboratories that relate somewhat to this
material:
Standing Waves and Acoustic
Resonance (core)
The Speed of Light
(non-core)
Spectra (core)
Suggested Supplemental Problem from Waves Assignment 3 – Not for marks
An object of mass, m=16 kg is
hung from a string, which passes over a light, frictionless pulley. The other end of the string is connected to a
vibrator, which sends waves along the string with a constant frequency, f.
It has been found that 20 metres of this kind
of string, when coiled up and placed on a scale, has a mass of 40 grams. The distance between the point where the
string is tied to the vibrator and the point where the string touches the
pulley is L=2.0 m.
A)
What is the
linear mass density of the string?
B)
What is the
tension of the string between the pulley and vibrator?
C)
What is the speed
of waves on the string between the pulley and vibrator?
Note that the vibrator forms
an anti-node of the standing wave, and the point where the string touches the
pulley forms a node. This makes the
standing wave on this string similar to a standing wave in an air column that
is closed at one end.
D)
What is the
fundamental (n=1) frequency of
standing waves on the string?
E)
What is the
wavelength of the fundamental frequency?
F)
What is the
frequency of the n=5 mode of
vibration? Sketch the appearance of the
string in this mode, indicating positions of nodes and antinodes.