Variations in the electric field of a light wave are shown in the graph below. What is the wavelength of the wave?
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In this case, you are given information about the period (and therefore frequency) of a wave and asked for the wavelength of that same wave. Frequency and wavelength are very closely related and so this is just a definition problem.
The period of a wave is the time that it takes for an oscillator to go through one complete cycle. Because the graph of the wave shows time and not distance, you cannot read the wavelength from the graph directly. Instead, the graph is a depiction of the wave's period.
Frequency is the inverse of period: f = 1/T. In other words, if it takes one fourth of a second for an oscillator to go through one complete cycle, it goes through four cycles each second.
I am not given any numbers. How can I identify the problem type?
As always, focus on the relationships and not on what is given or requested. In this case, you are given time information through the graph and you know that time and wavelength are very closely related. You can find numbers from the graph and from your book (or the web) as you need them.
Can't I just read the answer from the graph?
No. The graph provides direct information about the period of the wave, and you are asked about wavelength.
A picture representing the wave properties is already provided. No further picture is necessary.
Wavelength and frequency are closely related quantities, and the relationship is given through the wave equation:
How did you know to relate wavelength and frequency?
You are provided information about the period of the wave in the graph. It is good to know and remember that if you know period you also know frequency. And of course the problem directly asks about wavelength.
Although the graph provides information about period, or the time it takes an oscillator to go through one complete cycle, you know that period and frequency are just the inverse of each other.
v in this case refers to the wave velocity.
λ is the symbol used for wavelength of a wave.
The wavelength of this light wave is 6000 nm.
Remember that frequency and period are the inverse of each other. Because you can read period off of the graph, I replaced f with 1/T.
Regardless of wavelength or period, the velocity of a light wave in air is 3.0 x 108 m/s.
The period of a wave is the time it takes to make one complete oscillation. This information can be read directly off the graph.
Wavelengths of light are typically tabulated in nanometers. 1 nm = 10-9 m.
As long as you recognize that period and frequency are inverses of each other, and that they are closely related to the wavelength of a wave, this is a straightforward single-step problem. Be careful not to assume that the graph shows wavelength directly--make sure to always read the axis.
Visible light has wavelengths from about 400 to 700 nm. This is a longer wavelength. If you check the electromagnetic spectrum, you will see that this is in the infra-red range.
What is the amplitude of the wave? It isn't given.
It doesn't matter. Amplitude is independent of wavelength and period. Amplitude related to intensity (brightness) of the wave, while wavelength and period related to the color.
I don't understand the reference to electric field. What is that?
If you have not yet studied electromagnetic waves, you won't know that the wave nature of light comes about from oscillating (changing) electric and magnetic fields. For the purpose of this problem, you just need to see that something is oscillating in the wave and it doesn't actually matter what the oscillator happens to be. You will study electric fields more completely later in your course.