Physics I Problems PDF
Physics I Problems PDF
Physics I Problems PDF
545
16.28 .. BIO The Vocal Tract. Many opera singers (and some
pop singers) have a range of about 2 12 octaves or even greater. Suppose a sopranos range extends from A below middle C (frequency
220 Hz) up to Eb-at above high C (frequency 1244 Hz). Although
the vocal tract is quite complicated, we can model it as a resonating
air column, like an organ pipe, that is open at the top and closed at
the bottom. The column extends from the mouth down to the
diaphragm in the chest cavity, and we can also assume that the
lowest note is the fundamental. How long is this column of air if
v = 354 m>s? Does your result seem reasonable, on the basis of
observations of your own body?
16.29 .. A certain pipe produces a fundamental frequency of
262 Hz in air. (a) If the pipe is lled with helium at the same temperature, what fundamental frequency does it produce? (The molar
mass of air is 28.8 g>mol, and the molar mass of helium is
4.00 g>mol.) (b) Does your answer to part (a) depend on whether
the pipe is open or stopped? Why or why not?
16.30 . Singing in the Shower. A pipe closed at both ends can
have standing waves inside of it, but you normally dont hear them
because little of the sound can get out. But you can hear them if you
are inside the pipe, such as someone singing in the shower. (a) Show
that the wavelengths of standing waves in a pipe of length L that is
closed at both ends are ln = 2L>n and the frequencies are given by
n = nv>2L = n1, where n = 1, 2, 3, . (b) Modeling it as a
pipe, nd the frequency of the fundamental and the rst two overtones for a shower 2.50 m tall. Are these frequencies audible?
16.31 . You blow across the open mouth of an empty test tube
and produce the fundamental standing wave of the air column
inside the test tube. The speed of sound in air is 344 m>s and the
test tube acts as a stopped pipe. (a) If the length of the air column
in the test tube is 14.0 cm, what is the frequency of this standing
wave? (b) What is the frequency of the fundamental standing wave
in the air column if the test tube is half lled with water?
16.32 .. CP You have a stopped pipe of adjustable length close to
a taut 85.0-cm, 7.25-g wire under a tension of 4110 N. You want to
adjust the length of the pipe so that, when it produces sound at its
fundamental frequency, this sound causes the wire to vibrate in its
second overtone with very large amplitude. How long should the
pipe be?
Figure E16.33
P
x
2.00 m
1.00 m