Measuring waves

A wave is a travelling disturbance that transfers energy. To describe its motion, compare the direction the wave travels with the direction of vibration. In a transverse wave, these directions are at right angles. In a longitudinal wave, they are parallel.

Ripples spreading across a water surface provide a visible model of a transverse wave: crests move across the tank while the surface rises and falls. Sound in air is longitudinal. As sound travels, air is alternately compressed and spread out, producing moving compressions and rarefactions. The air vibrates back and forth along the direction in which the sound travels.

Measuring the speed of water ripples

A ripple tank is a shallow, clear-bottomed container of water. A vibrating bar can produce a regular train of ripples whose crests are easy to see. Wave speed means the distance a crest travels per second. Place a ruler alongside the direction of travel and record the ripples with a timer visible in the recording. On playback, follow one crest between two positions and measure the distance travelled, $d$, and the elapsed time, $t$. Then calculate $v=d/t$, using metres and seconds to obtain metres per second (m/s).

For regular ripples, there is another route. Measure the distance across several successive crest-to-crest gaps and divide by the number of gaps to estimate the wavelength, $\lambda$. Find the frequency, $f$, in waves per second from the vibrating bar or by counting crests passing a fixed point over a measured time. Then use $v=f\lambda$. Measuring several wavelengths reduces the effect of an error in locating any one crest. Both methods measure how quickly the ripple pattern travels across the water.

Measuring the speed of sound in air

Sound travels too quickly for its compressions to be followed by eye. An echo provides a measurable journey: a short sound travels to a large wall and reflects back. Measure the distance $d$ from the sound source to the wall. Start timing when the sound is made and stop when its echo is heard. The sound has travelled $2d$, so its speed is

$v=\frac{2d}{t}.$

Use a wall far enough away that the original sound and echo can be distinguished, and repeat the timing to check the result. Sound travels at about 340 m/s in air, though its speed varies with conditions such as temperature. The echo method measures the travel of the sound wave in air, just as tracking a crest measures the travel of a ripple across water.