Wave Speed – the distance a wave travels per unit time.
From kinematics we know that speed is equal to the distance an object travels per unit time. This equation can be applied to waves.
For waves we can calculate the speed (v) by using the wavelength as the distance and the time period as the time. This gives us the following equation:
Where λ is the wavelength measured in metres (m) and T is the time period measure in seconds (s).
The units for wave speed are metres per second (ms-1) – the SI units for speed.
Frequency
The frequency (f) of a wave is the number of oscillations per unit time, calculated using the following equation:
We can use this equation to find an equation for wave speed in terms of the wavelength and the frequency of a wave. If we rearrange the above equation for the time period we get:
We can now substitute this into the equation for wave speed to get:
The units for wave speed remain the same because the SI unit for frequency is per second (s-1).
From this equation we can see that wavelength is inversely proportional to frequency. This means as wavelength increases, frequency decreases.
Medium
If the medium a wave travels through remains the same the speed of the wave will also remain constant.
Wave speed can only be changed by a change in medium (such as from air to water) or a change in the mediums properties (such as increasing the temperature or density of the medium).
This means that changing the frequency (or wavelength) of a wave will not result in a change in wave speed. If you increase the frequency the wavelength will decrease and the wave speed will remain the same.
Electromagnetic Waves
All electromagnetic waves travel at the speed of light in a vacuum – approximately 2.998×108 ms-1. We can substitute the speed of light (c) into the equation:
This equation can be used for light and any other electromagnetic wave travelling through a vacuum. If the wavelength or frequency is known, the other can be easily calculated.
Worked Examples
Example 1
The wavelength of a wave is 2m. If the speed of the wave is 0.5 ms-1 calculate the time period of the wave.
Example 2
An x-ray travelling through a vacuum has a frequency of 3 x1016 Hz. Calculate the wavelength of this x-ray.
Use 3 x108 ms-1 for the speed of light.
This question requires knowledge of the electromagnetic spectrum.
Example 3
Calculate the speed of a wave with a frequency of 10Hz and a wavelength of 5m.
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