General comments:
To solve these problems, you usually need to convert the wavelenth to meters before using λν = c. The reason for meters is that, to solve these type of problems, using 3.00 x 108 m s¯1 for the speed of light is usually the best choice.
That being said, there are problems worded in such a way for which 3.00 x 1010 cm s¯1 (for the speed of light) is the better-suited value. Some examples are below. Sometimes a teacher might supply the centimeter value in the problem, but the meter value would be better suited for the solution. Be careful on your units!
Often, these problems require metric conversions. If you wish to review metric conversions, click here.
Problem #1a: Calculate the frequency of radiation with a wavelength of 442 nm.
Example #1b: The wavelength of an argon laser's output is 488.0 nm. Calculate the frequency of this wavelength of electromagnetic radiation.
Solution to 1a:
1) Convert nm to m:442 nm x (1 m / 109 nm) = 4.42 x 10¯7 m
2) Substitute into λν = c:(4.42 x 10¯7 m) (x) = 3.00 x 108 m s¯1
x = 6.79 x 1014 s¯1
Solution to 1b:
1) Convert nm to m:488 nm x (1 m / 109 nm) = 4.88 x 10¯7 m
Then, substitute into λν = c:(4.88 x 10¯7 m) (x) = 3.00 x 108 m s¯1
x = 6.15 x 1014 s¯1
The use of nm for wavelength is quite common.
Problem #2a: Calculate the frequency of electromagnetic radiation that has a wavelength of 1.315 micrometers.
Problem #2b: What is the frequency of infrared radiation of wavelength 67.5 μm?
Solution to 2a:
1) Convert μm to m:1.315 μm x (1 m / 106 μm) = 1.315 x 10¯6 m
2) Substitute into λν = c:(1.315 x 10¯6 m) (x) = 3.00 x 108 m s¯1
x = 2.28 x 1014 s¯1
Solution to 2b:
1) Convert μm to m:67.5 μm = 67.5 x 10-6 m
2) Use λν = c to determine the frequency:(67.5 x 10-6 m) (x) = 3.00 x 108 m/s
x = 4.44 x 1012 s-1
Problem #3a: Calculate the frequency of radiation with a wavelength of 4.92 cm.
Problem #3b: Calculate the frequency of radiation with a wavelength of 4.55 x 10¯9 cm.
Comment: since the wavelengths are already in cm, we can use c = 3.00 x 1010 cm s¯1 and not have to do any conversions at all.
Solution to 3a:(4.92 cm) (x) = 3.00 x 1010 cm s¯1
x = 6.10 x 109 s¯1
Solution to 3b:(4.55 x 10¯9 cm) (x) = 3.00 x 1010 cm s¯1
x = 6.59 x 1018 s¯1
Problem #4: Calculate the frequency of radiation with a wavelength of 8973 Å.
Comment: since 1 Å = 10¯8 cm, therefore 8973 Å = 8973 x 10¯8 cm. Converting to scientific notation gives 8.973 x 10¯5 cm. This is another place where the cm s¯1 value for c can be used, since Å converts to cm very easily.
Solution:(8.973 x 10¯5 cm) (x) = 3.00 x 1010 cm s¯1
x = 3.34 x 1014 s¯1
Example #5: What is the frequency of radiation with a wavelength of 5.00 x 10¯8 m? In what region of the electromagnetic spectrum is this radiation?
Solution:
1) Use λν = c to determine the frequency:(5.00 x 10¯8 m) (x) = 3.00 x 108 m/s
x = 6.00 x 1015 s¯1
2) Determine the electromagnetic spectrum region:Consult a convenient reference source.
This frequency is right in the middle of the ultraviolet region of the spectrum.
Wave speed = (wavelength) x (frequency) "Depth" (?) is not involved.
wave length = wave speed divided by its frequency
velocity = frequency multiply wavelength Rearrange the equation to find the frequency
The answer depends on the units used for .45 and since these are not given, there cannot be a sensible answer.
The product of (wavelength x frequency) is the wave's speed.
(frequency) multiplied by (wavelength) = (speed of the wave)
The velocity of the light waves must be given before the frequency can be find.
the velocity of a wave is given by frequency*its wavelength
To get the wavelength of a wave simply divide the wavespeed with its frequency.
You can use the equation v=fw. that is velocity (in meters per second) equals the frequency (in hertz) times the wavelength (in meters). so you can find the velocity of a wave with the frequency and the wavelength.
Frequency (f)=Speed of the wave(v)/wavelength l
v=fλ where f is the frequency, and λ is the wavelength
Answer: frequency = 272 Hz. Given the wave velocity (speed of sound) and wavelength, find the frequency of the wave. Velocity = 340.0 m/s, Wavelength = 1.25 m. Formulas: Velocity = wavelength * frequency. Frequency = velocity / wavelength. Calculation: Frequency = (340.0 m/s) / (1.25 m) = 272 Hz. (Where Hertz = cycles / second.)
Wave speed = (wavelength) x (frequency) "Depth" (?) is not involved.
. . . reduces by half.
Wavelength = wave speed/frequency Frequency = wave speed/wavelength (Wavelength) x (Frequency) = Wave speed
Frequency = (wave speed) divided by (wavelength)Wavelength = (wave speed) divided by (frequency)Wave speed = (frequency) multiplied by (wavelength)