Estimating wavelength, frequency, and velocity of ripples
Students derive the wave equation, by closely observing ripples in a ripple tank.
Apparatus and materials
For each group of students
Motor mounted on beam, with beam support
Stopwatch or stopclock
Health & Safety and Technical notes
Beware of water on the laboratory floor. Make sure you have a sponge and bucket handy to mop up spills immediately.
Place the power supply for the lamp on a bench, not on the floor by the tank.
In all work with flashing lights, teachers must be aware of any student suffering from photo-induced epilepsy. This condition is very rare. However, make sensitive inquiry of any known epileptic to see whether an attack has ever been associated with flashing lights. If so, the student could be invited to leave the lab or shield his/her eyes as deemed advisable. It is impracticable to avoid the hazardous frequency range (7 to 15 Hz) in these experiments.
The white paper is used as a screen on the floor.
Wave velocity is very difficult to measure except for low frequency ripples of long wavelength. Therefore, the vibrator should be adjusted to the lowest frequency.
Generate continuous straight waves, running the motor-driven beam as slowly as possible to produce low frequency ripples of long wavelength.
Freeze the wave pattern using a stroboscope.
Find the wavelength by measuring a batch of wavelengths (say ten) on the paper on the floor and finding the average.
Count the number of vibrations in a given time interval (perhaps in groups of four). One way to do this: let a thin piece of paper just touch the spindle of the vibrator, to make audible sounds. This should not slow the motor much.
Calculate the number of waves per second.
For higher frequencies, observe the rotation of the motor using a hand stroboscope.
One student should run a pencil along the paper, keeping it level with one wave. Another student measures the time taken to travel between the two points marked on the paper.
Calculate speed = distance / time
NOTE: The velocity of wave pulses is easier to measure but they do not travel at the proper wave speed, so is not appropriate.
1 It should be possible to calculate whether frequency x wavelength is near to the measured value for the velocity.
2 Estimating wavelength: Make clear that the idea is to get a rough estimate rather quickly, and not to try to achieve great precision with a technique which cannot really support it.
3 An easy way to introduce the wave equation is the following. Walking at 50 strides a minute, with each stride 0.5 metres long, then a distance of 25 metres can be covered each minute. The number of strides per minute is the frequency of the stride and when it is multiplied by the length of the stride then the velocity of the walker has been calculated. Similarly with wave motion so thatvelocity = wavelength x frequency.
4 The wavelengths and speeds that are measured are not those of the ripples but those of their shadows on the floor. This does not matter if measurements on the floor are used consistently; but measurements on the water can be calculated by proportion, if students prefer that. Only able students, who bring it up, need to discuss it.
5 NOTE: Wave speed is a function of the wavelength for water waves. In other words, water is a ‘dispersive medium’. The wave speeds that students measure will differ, depending on the frequency of their vibrator.
6 You could go on to look at other waves such as radio waves: work from the published wavelengths and frequencies to calculate the velocity of the waves.
This experiment was safety-checked in February 2006