Measuring waves

Choosing and using measuring apparatus

A measurement is useful only if the apparatus suits both what you are measuring and how large it is. For length, use a tape measure for a long distance, a ruler for a shorter one and callipers for a small diameter. Read a scale straight on to avoid parallax error, and choose an instrument with fine enough divisions to distinguish the changes you expect. Record the value with its unit.

Some quantities are found from other measurements. Measure the relevant lengths and calculate the area of a regular shape. Use a balance for mass, checking that it reads zero before adding the object. A stopwatch measures time, although starting and stopping it by hand introduces reaction-time variation. To find the volume of an irregular solid, put water in a graduated measuring cylinder and record its initial volume. Fully submerge the solid, then record the final volume; the difference between the two readings is the solid’s volume. Read the water level at eye height. Measure temperature with a thermometer. If measuring a liquid, stir it gently first so that the temperature is more uniform. Using suitable apparatus carefully matters as much as choosing it.

What needs measuring in a wave

A wave pattern gives you two different kinds of information. Wavelength, $\lambda$, is a distance along the direction the wave travels: for water waves it can be measured from one crest to the next. Frequency, $f$, tells you how many complete waves pass a point each second. Once both are known, calculate the wave speed, $v$, using

$v=f\lambda$

Use frequency in hertz (Hz) and wavelength in metres (m) to obtain speed in metres per second (m/s). Watching the pattern first helps you decide whether a ruler, a timer or a generator reading is the most suitable way to obtain each quantity.

Water waves in a ripple tank

A ripple tank makes waves in a fluid visible. A vibrating straight rod touches shallow water to produce a series of straight wavefronts. A lamp can project their pattern onto white card beneath the tank. Observe the pattern before measuring: the wavefronts must be clear enough to identify and count.

Place a ruler at right angles to the wavefronts, along the direction the waves travel. Measure across several complete wavelengths, then divide the total distance by the number of wavelengths. If you measure a projected image rather than the water itself, account for any enlargement so that the wavelength represents the distance in the tank. At a low frequency, count how many wavefronts pass one fixed point during a timed interval; divide the count by the time in seconds to find the frequency. Calculate speed from $v=f\lambda$.

Waves on a stretched string

A stretched string or elastic cord is a solid through which a wave travels. A vibration generator can make a visible pattern on it. The vibrating length and the tension can be adjusted until the pattern is clear. The frequency is read from the signal generator driving the vibration generator.

The visible loops on the string are half-wavelengths. Measure across several loops with a ruler. Divide that length by the number of loops to find one half-wavelength, then multiply by two to obtain $\lambda$. As in the ripple tank, use the measured wavelength and frequency to calculate speed. The two arrangements show why the apparatus must suit the pattern: travelling water wavefronts can be counted as they pass a point, whereas the string’s visible loops are measured as half-wavelengths.

Apparatus

Match the instrument and its resolution to the quantity and size: ruler, tape measure or callipers for length; measured lengths for calculated area; balance for mass; stopwatch for time; initial and final readings in a graduated measuring cylinder for an irregular solid’s volume; thermometer for temperature. Check zero, read scales straight on and record units.

Measuring waves

$\lambda$ is the distance between corresponding points on successive waves; $f$ is complete waves per second. In a ripple tank, measure across several wavefronts and count waves passing a point in a timed interval. On a vibrating string, each visible loop is half a wavelength; read frequency from the generator. In either case, $v=f\lambda$ (m/s when $f$ is in Hz and $\lambda$ in m).