Investigate wave speed, frequency and wavelength in a liquid and a solid. A ripple tank shows water waves; a vibrating metal rod provides a solid-wave investigation. A string demonstration alone does not fulfil the solid-rod part.Original labelled apparatus schematic; not to scale. Follow the stated measurements and safety instructions.
Use shallow water, a straight vibrating dipper, lamp, screen or projected image and a ruler for the ripple tank. The dipper frequency must be known or measured rather than guessed.
For the rod, use a supported or suspended metal rod and suitable vibration sensor/microphone/data logger to determine frequency. A known standing-wave mode can link rod length to wavelength; use the mode specified by the apparatus.
Keep electrical equipment dry, secure the rod and protect hearing from loud sounds. Use only a suitable school setup and modest vibration amplitudes.
Liquid method and solid method
Keep water depth constant and let disturbances settle. Set a steady dipper frequency and generate parallel crests so separation can be measured perpendicular to the wavefronts.
Measure the distance across several complete wavelengths between equivalent crests, then divide by the number of intervals, not the number of crest lines. Repeat at several positions.
Use a stationary-looking image from a suitable strobe or photograph if provided. Check the strobe frequency corresponds to the wave frequency: apparent stillness can occur at other settings too.
A projected image may be enlarged. Measure a reference length at the water surface and its projection to correct the wavelength scale; do not assume the screen spacing is the actual water spacing.
Find frequency by counting complete vibrations (oscillations or cycles) over a measured time, or use a calibrated generator or sensor. Frequency = number of cycles ÷ time. For the waves produced, this is the number of complete waves per second. Period T = time ÷ number of cycles, and f = 1/T.
Calculate water-wave speed with v = fλ, using actual wavelength in metres and frequency in hertz. An alternative is timing a crest over a known distance when individual crests can be followed reliably.
Make the rod vibrate longitudinally using the instructed support and striking or rubbing method. Detect a clear vibration pattern (mode). Check which mode it is: not every peak in a frequency reading is the lowest-frequency pattern (the fundamental).
For a rod with both ends free, the lowest-frequency longitudinal vibration (the fundamental mode) fits half a wavelength along the rod. Therefore L = λ/2, λ = 2L and v = 2Lf. Different supports or vibration modes change this relationship; use the mode specified for your apparatus.
Repeat the frequency measurement and measure rod length accurately. A frequency spectrum shows peaks for the fundamental and higher-frequency patterns (harmonics), helping you tell them apart. Keep rod material and temperature the same when comparing lengths.
In water, you can measure wavelength directly between crests. In the rod, you work it out from rod length and an identified vibration mode. Explain the assumptions for each method and the limits of the instruments.
Evaluation and interpretation
More wavelengths in one distance reduce relative ruler uncertainty. Use a clear crest reference, avoid parallax and distorted images, and do not count crest-to-trough spacing as a full wavelength.
Timing many cycles reduces the relative effect of human reaction time. Electronic detection can measure shorter time intervals, but still needs calibration and correct identification of frequency peaks.
Changing water depth changes wave speed, so varying frequency requires depth control. If speed is roughly constant, increased frequency corresponds to shorter wavelength.
Waves transfer energy. Water and rod particles vibrate back and forth (oscillate) around their rest positions; they do not travel across the apparatus with the wave.
A wavelength error from projection magnification or a mistaken harmonic is systematic. Repeats of the same mistake do not fix it.
In an exam answer, use measured frequency f and wavelength λ with units. Include a diagram showing the vibration mode you used. Explain whether you measured wavelength directly or worked it out from the apparatus dimensions.
Exam skills: planning, precision and evaluation
State what you change (the independent variable), what you measure (the dependent variable) and what you keep the same (control variables). Explain how you keep each control variable constant, rather than just saying “make it fair”.
Accuracy means how close a result is to the true value. Precision means how close repeated measurements are to each other. Resolution is the smallest change an instrument can show. More digits on a display do not automatically mean a more accurate result.
Repeat measurements for each condition, calculate a mean and describe how spread out the results are. This helps assess and reduce the effect of random errors. Repeating cannot fix an error that pushes results consistently in one direction (a systematic error), such as using enlarged projected crest spacing without correcting the scale.
Repeatability means getting similar results when the same person repeats the same method with the same equipment. Reproducibility means getting similar results when someone else, or different suitable equipment, repeats the experiment. Results can be consistent but still inaccurate.
Check that instruments read zero correctly and are calibrated where needed. Read scales at eye level: looking from an angle can give a wrong reading (parallax error). Choose suitable ranges, measurement intervals and scale divisions (resolution).
Write down the original readings straight away in a table, with units in the headings. Use decimal places that match the instrument’s resolution. Keep the original data and round only when needed. Do not discard a result just because it differs from your prediction.
An anomalous result does not fit the pattern of the other results. Repeat that measurement and check the method. Only leave it out of a mean if you have a clear reason; state which result you excluded and why.
For continuous variables, plot the independent variable on the horizontal axis and the dependent variable vertically. Use sensible scales, units and a best-fit line or curve; do not automatically join every point or force the graph through zero.
Find the gradient of a straight best-fit line using a large triangle: vertical change ÷ horizontal change. For a curve, draw a tangent to estimate the gradient at one point. Explain what the gradient shows in this experiment, include its units and use measured values to support your conclusion.
Uncertainty describes the possible range around a measurement. For one reading on a scale, half the smallest division is a useful classroom estimate unless the question says otherwise. If you subtract two readings, both have uncertainty. Percentage uncertainty = absolute uncertainty ÷ measured value × 100. Follow the method specified in the question.
Use results as evidence and then explain what they mean. A pattern linking variables (a correlation) does not prove that one causes the other. If the ranges of repeat results overlap, a claimed difference may be less convincing. Keep conclusions within the range tested and suggest an improvement that tackles a specific error.
Mr Kidman's Classroom