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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.

Q: How do you find the frequency of a wave if you are given the wavelength?

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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.

Related questions

To calculate frequency when given a half-wavelength, you first find the full wavelength by doubling the half-wavelength value. Then, use the formula frequency = speed of wave / wavelength to find the frequency of the wave.

(frequency) multiplied by (wavelength) = (speed of the wave)

If the frequency doubles, the wavelength is halved. This is because frequency and wavelength are inversely proportional in a wave. This relationship is described by the formula: frequency x wavelength = speed of the wave.

The speed of a wave is equal to the product of its frequency and wavelength. This relationship is given by the formula: speed = frequency × wavelength. So, if the frequency of a wave increases while the wavelength stays the same, the speed of the wave will also increase.

When the wavelength of a wave increases, the frequency decreases. This is because frequency and wavelength are inversely proportional in a wave. A longer wavelength means fewer wave cycles can fit in a given period of time, resulting in a lower frequency.

To get the wavelength of a wave simply divide the wavespeed with its frequency.

To find the frequency of a wave, you need to know the number of complete wave cycles that pass a point in a given time, usually measured in hertz (Hz). You can calculate the frequency by dividing the speed of the wave by its wavelength.

To find the wavelength, you can use the formula: wavelength = speed of wave / frequency. Given that the wave is traveling at 56 m/s and has a frequency of 48 Hz, you can calculate the wavelength by dividing the speed (56 m/s) by the frequency (48 Hz), which gives you a wavelength of approximately 1.17 meters.

The velocity of the wave

The relationship between wave speed, wavelength, and frequency is given by the equation: wave speed = frequency x wavelength. This means that as frequency increases, wavelength decreases, and vice versa, while wave speed remains constant. If wave speed changes, then frequency and wavelength must also change proportionally.

wavelength by using the formula: Velocity = frequency x wavelength. The frequency indicates how many wave cycles pass a fixed point in one second, while the wavelength is the distance between two consecutive points in a wave that are in phase. By multiplying the frequency by the wavelength, you can determine the speed at which the wave is traveling.

When the frequency of a wave is doubled, the wavelength is halved. This is because the speed of a wave is constant in a given medium, so an increase in frequency results in a decrease in wavelength to maintain a constant speed.