We have already briefly looked at some of the properties of a wave, now I want to move into a little bit of the mathematics of waves.


From the section on transverse waves, the diagrams there shows the amplitude and wavelength of a wave. Just to recap the amplitude is the maximum displacement from the rest position (the baseline), and the wavelength is the distance between two "matching" points on the wave, in other words the distance between two peaks, two troughs et cetera.


How many waves passing a certain point in a certain amount of time will give us an idea of the frequency of the wave. How long a "full wave cycle" takes to complete (once again, peak to peak or trough to trough et cetera) will determine the period of the wave.



The velocity of a wave is the number of complete waves per second multiplied by the wave length. In the above case, suppose that the wavelength was 10 metres. We can see that the period is 4 seconds and so we only get a quarter of a whole wave per second. If we put these values into an expression we can evaluate the wave speed:


Wavelength (Lambda λ ) = 10m
Period = 4s

Frequency = 0.25 cps (Hz)


Q. A "ripple tank" is used to produce waves on water. In a particular instance waves are produced with a wavelength of 10 cm, and 5 waves are produced each second. From this information calculate the velocity of the wave.


A. First of all, make sure that the information you've been given is in the correct units. We measure wavelength in metres so the first thing that we must do is convert 10 cm to metres, this is 0.1 m. We are told that the tank produces five waves per second therefore it is operating at a frequency of 5 Hz.


So far we've looked at long wavelength radiation, such as radio waves. We go to the other end of the spectrum and start looking at visible light, or beyond (into the realms of gamma rays) we will be using some very short wavelength and high-frequency waves.


Q. The wavelength of the red light emitted from a laser pen is 650 nm, given that the speed of light in a vacuum is 3×108 metres per second, calculate the frequency of this red laser light.


A. We must first of all convert our wavelength from nanometres into metres. 1 m = 109 nm so our laser light has a wavelength of 650 x 10-9 m. Ideally we should convert this to 6.50×10-7 m but we can continue as we are, making sure that we quote our answers to the correct scale at the end.


The velocity of light is given as 3 x 108 m/s.




Q. A light wave has a wavelength of 7.5 x 10-7 m and travels at 3.0 x 108 m/s. What is its frequency?


A.



The speed (or velocity) of light and sound varies depending on the medium (ie: what it is travelling through). Sound waves are compression waves and so they need a medium (air, water, solid) to travel through by vibration of particles. Light waves are transverse and not dependent on a medium to travel through.




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