Standwaves

Royal Grammar School
Physics Department
A Level Core Practical
Title:
CP7 - Standing Waves
Aim:
To investigate the effects of length, tension and frequency on the mass per unit length of a vibrating wire.
Underlying Physics (what equations applies, what graph will you plot?) :
The equations v=f λ as well as v=

√ T apply. These can then derive the equation λ 2= 1 T , where λ is the
μ μf2
wavelength of the standing wave, measured as the distance between two distances between nodes in the wire,
μ is the mass per unit length of the wire, f is the frequency of the wire which is kept constant throughout the
experiment, and T is the tension acting on the wire.
1
In the final equation, λ 2 will be plotted against T in order to produce a line with a gradient of 2 , which can
μf
then be used to find μ.
Prediction (will you get a straight line, why?) :
There will be a straight line because the frequency and mass per unit length remain constant.
Diagram of equipment: Explanation of equipment:

Meter ruler is used in order to measure the
wavelength of the first harmonic of the wire,
ensuring to account for fence-post error when
measuring the distance between multiple nodes.
The hanging masses provide tension to the system.
A signal generator produces a constant frequency
for the copper wire.
A pulley transfers the vertical components on the
tension horizontally across the wire.
Wires are placed to touch either end of the copper
wire in order to provide a frequency from the
frequency generator.
Bridges are used to measure the distance more
accurately between nodes.
Clamps are used to hold the wire touching the
copper wire as well as one end of the copper wire in
place.
A sheet of paper can be used to better identify the
location of the first harmonic.
A magnet is used in order to increase the amplitude
of the standing waves so that they are more visible.
Physics Department
Method:
- The equipment is set up as shown above, with a wire of SWG of 32 by tying it around a stand.
- Measure the weights of all of the hanging masses and the mass carrier beforehand using a ruler, in
addition to the length (ruler) and mass (mass balance) of the copper wire used.
- Tying the mass carrier to the end of the copper wire near the pulley, move the two bridges on either side
of the magnet to the points at which nodes form in the wire (areas of destructive interference), before
measuring the distance between the two bridges to obtain the wavelength using the meter ruler.
- Repeat the previous step three times in total, before adding another weight with known mass and
repeating with more tension in the copper wire.
Variables:
Dependant - Tension in the copper wire.
Independent - Wavelength of the first harmonic of the copper wire.
Control:
- The same wire needs to be used throughout.
- Frequency (the signal generator produces a constant frequency throughout).
Uncertainty or Error Impact on Experiment How to Minimise

Wavelength ±0.005 meters Measure the distance several times and take an
average, or use more precise equipment to measure
distance.
Hanging Masses ±0.05 grams Measure the masses several times and take an
average, or use a higher resolution balance.
Results:
Physics Department
Graph:
Physics Department
Analysis and evaluation (trends, physics, further analysis of gradients, calculations of uncertainties, anomalies,
errors and uncertainties contributing to imperfect results, improvements to minimise these + improve method,
conclusion regarding accuracy):
The standard mass per unit length for a copper wire with an SWG of 32 should be around 5.27e-4 gm⁻² - value
obtained from a Wikibook for standard wire gauges 1- and in this experiment, we managed to reach a value of
5.1e-4 gm⁻² with a percentage uncertainty of 0.5% which gives the final value of 5.1e-4 gm⁻² ±2.47e-6. This
means that the value we got was close but not particularly precise. This is likely due to inaccuracies during the
readings as it was a little difficult to accurately determine where the harmonics began and ended despite the
changes we made to the experiment to reduce as much human error as we possibly could. If we were to repeat
the experiment it may be a good idea to take a photograph of the harmonic so we are able to zoom into the
standing wave produced and therefore be able to more accurately determine where the harmonic began and
ended.
1
https://en.wikibooks.org/wiki/Engineering_Tables/Standard_Wire_Gauge

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Royal Grammar School

The equations v=f λ as well as v=

Diagram of equipment: Explanation of equipment:

Uncertainty or Error Impact on Experiment How to Minimise

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