(c) Suppose you could grab one of the atoms in a diatomic molecule
like H 2 or O 2 , and let the other atom hang vertically below it. Does
the bond stretch by any appreciable fraction due to gravity?
39 This problem has been deleted.
40 Many fish have an organ known as a swim bladder, an air-
filled cavity whose main purpose is to control the fish’s buoyancy
and allow it to keep from rising or sinking without having to use its
muscles. In some fish, however, the swim bladder (or a small exten-
sion of it) is linked to the ear and serves the additional purpose of
amplifying sound waves. For a typical fish having such an anatomy,
the bladder has a resonant frequency of 300 Hz, the bladder’sQis 3,
and the maximum amplification is about a factor of 100 in energy.
Over what range of frequencies would the amplification be at least
a factor of 50?
41 An oscillator with sufficiently strong damping has its max-
imum response atω= 0. Using the result derived on page 1024 ,
find the value ofQat which this behavior sets in.
.Hint, p. 1031 .Answer, p. 106442 An oscillator hasQ=6.00, and, for convenience, let’s assume
Fm= 1.00,ωo= 1.00, andm= 1.00. The usual approximations
would give
ωres=ωo,
Ares= 6.00, and
∆ω= 1/6.00.Determine these three quantities numerically using the result de-
rived on page 1024 , and compare with the approximations.43 The apparatus in figure d on page 61 had a natural period
of oscillation of 5 hours and 20 minutes. The authors estimated,
based on calculations of internal friction in the tungsten wire, that
itsQwas on the order of 10^6 , but they were unable to measure it
empirically because it would have taken years for the amplitude to
die down by any measurable amount. Although each aluminum or
platinum mass was really moving along an arc of a circle, any actual
oscillations caused by a violation of the equivalence of gravitational
and inertial mass would have been measured in millions of a degree,
so it’s a good approximation to say that each mass’s motion was
along a (very short!) straight line segment. We can also treat each
mass as if it was oscillating separately from the others. If the prin-Problems 229