Measuring Wave Properties

• Identify the requisite units for period (seconds, s) and frequency (hertz, Hz).
• Define wave speed as the exact velocity at which energy is transferred or the wave progresses through its medium.
• Apply the universal wave equation to calculate wave speed, frequency, or wavelength:

$v = f \lambda$

• Identify amplitude and wavelength variables actively from provided visual wave diagrams.
• Describe comprehensive methodologies to effectively measure the speed of sound waves propagating in air and the speed of ripples on a water surface.
• Make practical observations using a ripple tank and solid mediums to identify highly suitable apparatus for capturing measurements of frequency, wavelength, and speed.

A lamp above the transparent tank projects the wave pattern onto white card underneath. Adjust the lamp until the pattern is clear; dimmer room lighting can help. Look directly at the card from the side rather than down through the water.

Observe the pattern before choosing how to measure it. If the waves pass slowly enough to count, a stopwatch is suitable for frequency. If they are too fast to follow, a video recording can make counting easier. A stroboscope can also make the pattern appear stationary when appropriately matched to the wave frequency, but it must only be used after checking that flashing light will not affect anyone present.

Measuring ripple wavelength, frequency and speed

Place a metre ruler at right angles to the wavefronts, along the direction of wave travel. Measure from one crest to a later crest across several complete wavelength intervals. Divide this total distance by the number of intervals to obtain the mean wavelength. Measuring several intervals makes the uncertainty in locating the endpoints smaller relative to the total length measured.

To measure frequency, choose a fixed point in the pattern. Count the number of complete waves passing that point during a measured time, such as 10 seconds:

Repeat the count and calculate a mean. Keep the water depth and motor setting unchanged while measuring the frequency and wavelength for one result. Record both values, convert the wavelength to metres, and calculate $v = f\lambda$.

For example, a ripple-tank result with a frequency of 4.545 Hz and wavelength of 0.025 m gives a speed of approximately 0.114 m/s. This is the speed of the travelling ripple pattern, not the speed at which an individual point on the water moves up and down.

Measuring waves in a solid string

A stretched string or elastic cord provides a solid material in which to observe waves. Connect a signal generator to a vibration generator attached to the string. Support the string over a wooden bridge and a pulley, with hanging masses providing tension. A metre ruler measures the vibrating length.

Adjust the signal-generator frequency until a clear pattern of vibrating loops appears. The vibrating length can also be adjusted by moving the bridge, or the tension changed by adding or removing masses. This is a standing-wave pattern: the loops vibrate, but their positions remain fixed. Similar patterns occur on the strings of musical instruments.

Each loop spans half a wavelength. Measure the length across several loops, divide by the number of loops, and multiply by two:

Read the frequency from the signal generator rather than trying to count the rapid vibrations. Use this frequency and the measured wavelength to calculate wave speed. Although the loop pattern stays in place, $v = f\lambda$ gives the speed of waves travelling along the string.

Repeat for another clear pattern. When comparing different frequencies, keep the same string and hanging masses so that its tension stays unchanged. Results of 10.0 Hz with a wavelength of 1.68 m, and 15.0 Hz with a wavelength of 1.12 m, both give 16.80 m/s: a higher frequency can be accompanied by a shorter wavelength without changing the speed.

Using the apparatus safely

Use a suitable low-voltage supply for the ripple tank and keep water away from electrical connections. For the string experiment, keep clear of hanging masses and use a soft surface underneath them in case they fall. Wear eye protection where a tensioned cord could snap.

Solid string

• Signal generator → vibration generator → stretched string; hanging masses provide tension.
• Adjust until clear vibrating loops form.
• Each loop is $\lambda/2$, so $\lambda = 2L/n$ for $n$ loops.
• Read frequency from the signal generator; calculate $v = f\lambda$.

Units

Distance and wavelength: m · time: s · frequency: Hz · speed: m/s