# 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.

1. 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?
2. Perform a linear least squares fit of c^2 versus tension to further check this model.
3. Use the fitted slope to determine the linear mass density µ
4. 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: