Core practical: evaluating wave-measurement equipment

Here, $v$ is speed in m/s, $x$ is distance in metres, $t$ is time in seconds, $f$ is frequency in hertz (Hz), and $\lambda$ is wavelength in metres. The second equation works because each complete wave advances the pattern by one wavelength: the number of waves per second multiplied by the length of each wave gives distance per second.

Measuring ripples on water

Use a ripple tank, a motor-driven straight dipper, a ruler and a stopwatch. A digital camera, if available, helps with measuring wavelength. Place the dipper near a short side of the tank and fasten the ruler along a long side, with its markings visible above the water. Adjust the motor until the wavelength is about half the tank's length, so that two waves can be seen.

Measure the wave properties in three ways:

1. Frequency: count the number of complete waves formed in 10 s. Divide this count by 10 to obtain the frequency in Hz. Counting over several seconds is more reliable than trying to count waves in just one second, because a small counting or timing error has a smaller relative effect.
2. Wavelength: use the ruler to measure the separation of neighbouring crests, along the direction in which the waves travel. A photograph taken with a ruler just above the waves freezes their positions, making the crest locations easier to judge.
3. Distance and travel time: mark two positions on the tank edge along the direction of travel. Measure their separation, then time a single crest travelling from the first position to the second. Calculate its speed using $v=x/t$.

Use your measured frequency and wavelength to calculate a second estimate of speed using $v=f\lambda$. These are two methods of measuring the same wave speed, so compare their results. They may differ because locating moving crests and starting or stopping a stopwatch introduce measurement uncertainty.

Mop up spilled water straight away, and keep water away from electrical equipment.

Improving the water measurements

A stopwatch may display hundredths of a second, but this does not mean a person can start and stop it that accurately. Resolution is the smallest change an instrument can distinguish; human reaction time can still limit a measurement made with a high-resolution instrument.

For direct speed measurements, use the greatest practical separation between the two marks. A longer journey gives a longer timing interval, reducing the relative effect of reaction time. Repeat the timing and calculate a mean to reduce the effect of random variation.

For wavelength, a clear photograph is useful because the waves no longer move while you read the ruler. If several complete wavelengths fit in view, measure their total length and divide by the number of wavelength intervals. Count the gaps between crests, not simply the number of crests.

Keep water depth and the motor setting unchanged while comparing the two speed methods. Water-wave speed depends on depth and wavelength, so groups using different depths or frequency settings need not obtain the same result. Sloping absorbing edges, often called beaches, help prevent reflected waves from confusing the pattern.

Measuring sound waves in a metal rod

Use a long metal rod, two clamps and stands, rubber bands, a hammer, a metre rule and a smartphone with a frequency app. Suspend the rod horizontally from the stands using the rubber bands, allowing it to vibrate.

Strike one end with the hammer. Hold the smartphone near the rod and record the peak frequency detected by the app. This measures the frequency of the sound produced by the vibrating rod without requiring you to count its rapid vibrations yourself.

Measure the rod's length, $L$, using the metre rule. For the vibration used in this method, the wavelength is twice the rod's length:

$$\lambda = 2L$$

Use this wavelength and the measured frequency in $v=f\lambda$ to calculate the speed of sound in the rod. This length–wavelength relationship is provided for the method; it is not a general rule for every vibration of every solid object.

A ruler is suitable for measuring the rod's length because the rod is stationary and its ends are identifiable. A frequency app is suitable for detecting vibrations too rapid to count by eye. By contrast, a handheld stopwatch cannot resolve the extremely short time sound takes to travel along a classroom-sized rod. Measuring the distance accurately would not overcome that timing problem.

Judging suitability from your measurements

Evaluation means explaining how well equipment performs its particular job, not simply saying that it is easy to use. Summarise both parts of the investigation using these headings:

For the rod, compare the quality of the length and frequency measurements rather than assuming one must be better. Consider how precisely the ends can be read, how much repeated readings vary, and whether background noise makes the frequency peak unclear. An app's many displayed digits do not by themselves establish accuracy.

Compare your two water-speed estimates and results from other groups. A useful conclusion identifies which equipment was suitable, what limited each measurement, and which practical change would improve it.

• Straight dipper produces waves; ruler gives the distance scale.
• Count waves formed in 10 s, then divide by 10 for frequency.
• Measure neighbouring crest separation for wavelength; a photograph helps freeze the pattern.
• Time a crest between two measured positions for $v=x/t$.
• Compare this speed with $v=f\lambda$.
• Repeat measurements; use longer timing intervals where practical. Keep depth and motor setting unchanged when comparing methods.

Solid: metal rod

• Suspend horizontally using rubber bands and two clamp stands.
• Strike one end; record the peak frequency with a smartphone app.
• Measure length $L$. For this method, use the supplied relationship $\lambda=2L$.
• Calculate sound speed using $v=f\lambda$.
• Direct travel time is too short for a handheld stopwatch.

Equipment evaluation

Judge suitability using resolution, repeatability and difficulties identifying the measured feature. Explain the limitation and a specific improvement. A digital display does not guarantee accuracy.