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Physics 107 - Standing Waves
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This experiment is another opportunity to perform a fit to a
linear data set and compare the result to a theoretical
expectation. You will be measuring the velocity of waves on a
wire under tension and then comparing to a model that involves
the linear mass density of the wire.
The velocity of transverse waves travelling along a wire under
tension is given by
c = sqrt(T/µ)
where T is the tension
(a force expressed in Newtons) and µ is the mass per unit length (linear mass
density expressed in kg/m).
You will be testing this model, and if it works, can then compare
µ to a direct
measurement of mass and length of the wire.
Instead of measuring the speed of a wave directly, you will measure
standing waves. The lowest harmonic standing wave on a wire occurs
when the length of the fixed wire matches half the wavelength of the
wave: lambda = length*2. If
you measure the resonant frequency at which this occurs, the
velocity can be determined from the wave equation c = frequency*wavelength.
- Use measurements of the standing wave frequency versus the
tension in the wire to check the power law model shown above. Is
a log-log plot of the data qualitatively consistent with the
square root behaviour?
- Perform a linear least squares fit of c^2 versus tension to
further check this model.
- Use the fitted slope to determine the linear mass density
µ
- Compare this mass density measurement to a direct measurement
of the wire which was found to be 2.2 g (on a digital scale) for
a more precisely measured length of 1.923 metres.
Tips:
- use up to 600g added to the holder
- plot your data and residuals as you go in order to check your
data and the model
- you can use frequency generator amplitudes up to 10 Volts to
search for resonances, but once you have found a resonance,
measure the frequency carefully at a much lower amplitude - 1
volt is typically enough amplitude to see the resonance and
avoids driving the wire too hard
Marking Scheme
12 marks for a high quality measurements of the wave
velocity, checking the model, and comparing the linear mass
density of the wire.
Don't forget to:
- justify your measurement uncertainty
- describe your measurement techniques
- provide well-labelled plots of your data, best fit of c^2 vs
T, and residuals
- give your value of Chi-squared and the best fit value of the
slope
- compare linear density measurements
- verify all of your steps and calculations
- confer with others and compare results