Homework 10
Due Sunday, May 9, by the end of the day
1. Suppose that the largest pipe in a pipe organ is 16 feet long, and the smallest pipe
is 0.25 feet long. The speed of sound in air is 1125 feet per second. What are the
fundamental frequencies of these two pipes?1 These figures are accurate (I believe) fo
the organ in Setnor Auditorium at Syracuse University.
2. The wave speed in a stretched string is given by v =
√
T
µ
, where T is the tension the
string is under, and µ is the linear mass density of the string in kilograms per meter.
Suppose that the vi
ating part of the highest-frequency string on a guitar has a length
of 72 cm and a linear mass density of 0.3 grams per meter. This string is usually tuned
to a fundamental frequency of 293 Hz. What tension must the body of the guitar apply
to the string in order to do this?
3. Draw pictures of the first six resonant modes of a vi
ating string. (We’ve drawn the
first few in class a few times.) Using the parameters of the previous problem (funda-
mental frequency of 293 Hz and vi
ating length of 72 cm), calculate the frequencies
and wavelengths of these six modes. Note: You should use an entire sheet of pape
for these drawings. (This exercise also appears on Wednesday’s recitation.)
4. The other strings in a guitar have the same length and about the same tension. Why do
they have lower fundamental frequencies? (Hint: What is different about the strings?
Look up a photograph of a guitar, and remember that v =
√
T
µ
.)
1Organists, even outside the US, still measure pipes in feet.
1