
Physics 107  Standing Waves

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 loglog 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 welllabelled plots of your data, best fit of c^2 vs
T, and residuals
 give your value of Chisquared 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