Workshop 12 - Physics 113, Fall 2007
Forced Oscillations, Damping, Waves
1. “In the case of a cock putting its head into an empty utensil of glass where it crowed
so that the utensil thereby broke, the whole cost shall be payable.”
- The Talmud (Baba Kamma, Chapter 2)
Meditate on this Talmudic pronouncement.
2. Take the simple pendulum given to your workshop leader and force it in an
oscillatory way by driving a lower part of the string back and forth. Can you observe
the reversal of the phase of the displacement as you move the driving frequency
through the natural frequency?
3. http://www.acoustics.salford.ac.uk/feschools/waves/wine1video.htm
Watch the slow motion video of a wine glass shattered by sound. When the driving
sound waves are in resonance with the wine glass, sketch the motion of the wine glass
excitations before it breaks.
4. Erving Von Humbolt, famed Professor of Pre-Columbian Artifacts has discovered a musical
instrument he believes was once used by native peoples in what is now southeast Paraguay.
Unfortunately, the instrument he has discovered is broken. He comes to you for help in
understanding what sounds the instrument might have made. Please help him out!
The instrument has one string. That string is tied at one end and constrained to move freely
up and down a thin rod on the other end. Break up into small groups and determine the
correct expression for the frequency of the nth harmonic of the string in terms of the length
(L), tension (T), and the mass/length () of the string. Try to convince the other groups of
your answer. Below are a few possibilities, one of which is the correct answer.
(a)
n 
(b)
n T
2L 
n 
(c)
n T
2L 
where n=1,3,5 …
where n=1,2,3, …
(d)
(e)
n 
n T
4L 
where n = 1,3,5, …
n 
n 
n
2L
gT

where n=1,2,3, …
n T
4L 
where n=1,2,3, …
5. On an electric guitar, a pickup under each string transform’s the string’s vibrations
into an electrical signal. If a pickup is placed 16.25 cm from one of the fixed ends of
a 65.0 cm long string, which of the harmonics from n=1 to n=12 will not be “picked
up”?