56
Experiment X:
Waves and Resonance
Goals
•
Study standing waves on a string under tension
•
Experimentally determine the relationship between velocity of wave propagation, tension in
the string, and the linear density of the string
Introduction and Background
Waves
:
A wave is the propagation of vibration in a medium. The velocity at which a
vibrational wave propagates through a medium depends not only on the properties of the medium,
but also on the external conditions imposed on it. For example, the velocity, V, with which a
transverse vibrational wave travels down a string or flexible wire would depend on the linear
density (mass per unit length),
μ
, of the string, as well as the tension, T, in the string. The tension
supplies the restoring force when the string is given a transverse displacement, and the linear
density determines the inertia of the string and thus its speed of response to the tension. Therefore,
we would expect that the velocity would increase with increasing tension and decrease with
increasing linear density.
Based on these arguments we can assume a power law relationship
between V, T and
μ
of the form
b
a
m
T
C
V
=
(101)
where
C
is a constant and
α
and
β
are the exponents. We expect
C
,
α
, and
β
to be positive integers
or simple fractions. As discussed in Experiment III (Centripetal Force), the standard way to
determine the power law exponents is to create a loglog plot and the slope of that plot would yield
the exponent.
Standing Wave
:
If you vibrate one end of a string and keep the other end fixed, a continuous
wave will travel down the string to the fixed end and be reflected back. Hence on the string there
will be waves traveling in both directions and they will interfere with each other. Usually this
results in a jumble. But with just the right combinations of the vibration frequency and tension in
the string, the two traveling waves will interfere in such a way that there will be a large amplitude
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 Fall '09
 LIND
 Physics, Wavelength, Standing wave

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