Required practical: investigating stationary waves on a string

Wave Types, Polarisation & Stationary Waves — AQA A-Level Physics

Aim

Measure how the frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). of the first harmonic varies with string length (or tension, or mass per unit length).

Setup

Attach one end of a string to a vibration generator connected to a signal generator.
Pass the other end over a pulley and attach a mass hanger to provide tension $T = mg$.
Place a moveable bridge between the vibration generator and the pulley to vary L.
Measure L with a metre ruler (resolutionThe smallest change in a quantity that an instrument can detect. For example, a ruler has a resolution of 1 mm. 1 mm).
Measure string mass with a top-pan balance (resolutionThe smallest change in a quantity that an instrument can detect. For example, a ruler has a resolution of 1 mm. 0.005 g) to calculate mu.

Method (varying length)

Set an initial length L (e.g. 0.2 m) and increase the signal generator frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). until the first harmonic is observed.
Record the frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz).. Repeat for different lengths up to about 1.6 m.
Take at least 3 readings at each length and calculate the mean frequency.
To find the first harmonic accurately: increase frequency past resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energyThe capacity to do work. Measured in joules (J). transfer., then slowly decrease until the largest vibration is seen again.

Analysis

Plot f (y-axis) against 1/L (x-axis). The relationship is $f = (v/2)(1/L)$, so the graph is a straight line through the origin.
$Gradient = v/2, so wave speedThe distance travelled by a wavefront per unit time. v = 2 \times gradient.$
Verify with $v = \sqrt{T/\mu}$ using independently measured T and mu.

Evaluation

Systematic: leave signal generator running for 20 minutes to stabilise. Verify with an oscilloscope.
Random: the sharpest nodeA point on a stationary wave where the displacement is always zero. Located at half-wavelength intervals. is the best indicator of resonanceThe condition where the driving frequency matches the natural frequency of a system, causing maximum amplitude of oscillation and maximum energyThe capacity to do work. Measured in joules (J). transfer.. Adjust frequency while watching a nodeA point on a stationary wave where the displacement is always zero. Located at half-wavelength intervals., not the antinodeA point on a stationary wave where the displacement is a maximum. Located midway between adjacent nodes. amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m)..
Use rubber string if possible. If using metal wire, wear goggles in case it snaps. Place a crash mat under the hanging masses.

Examiner Tips and Tricks

Always refer to the specific experiment in your answer.
For example: the wave from the vibration generator reflects at the bridge, and this reflected wave superposes with the original wave to create the stationary waveA wave pattern formed by the superposition of two progressive waves of the same frequency and amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). travelling in opposite directions. EnergyThe capacity to do work. Measured in joules (J). is not transferred along a stationary wave..