how to find period of a wave

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Wavelength is the distance of 1 frequency wave peak to the other and is most commonly associated with the electromagnetic spectrum.^[1] Calculating wavelength is dependent upon the information you are given. If you know the speed and frequency of the wave, you can use the basic formula for wavelength. If you want to determine the wavelength of light given the specific energy of a photon, you would use the energy equation. Calculating wavelength is easy as long as you know the correct equation.

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Calculate wavelength with the wavelength equation. To find the wavelength of a wave, you just have to divide the wave's speed by its frequency. The formula for calculating wavelength is: $Wavelength={\frac {Wavespeed}{Frequency}}$ . ^[2]
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Use the correct units. Speed can be represented using both metric and imperial units. You may see it as miles per hour (mph), kilometers per hour (kph), meters per second (m/s), etc. Wavelength is almost always given in metric units: nanometers, meters, millimeters, etc. Frequency is generally expressed in Hertz (Hz) which means "per second".^[3]
- Always keep units consistent across the equation. Most calculations are done using strictly metric units. If the frequency is in kilohertz (kHz) or the wave speed is in km/s you will need to convert these numbers to Hertz and m/s by multiplying by 1000 (10 kHz = 10,000 Hz).
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Plug the known quantities into the equation and solve. If you want to calculate the wavelength of a wave, then all you have to do is plug the wave's speed and wave's frequency into the equation. Dividing speed by frequency gives you the wavelength.^[4]
- For example: Find the wavelength of a wave traveling at 20 m/s at a frequency of 5 Hz.
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Use this equation to solve for speed or frequency. You can rearrange this equation and solve for speed or frequency if given wavelength. To calculate speed given frequency and wavelength, use $v={\lambda }*{f}$ . To calculate frequency given speed and wavelength, use $f={\frac {v}{\lambda }}$ .^[5]

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Rearrange to solve for wavelength. You can rearrange the equation with algebra to solve for wavelength. If you multiply both sides of the equation by wavelength and then divide both sides by energy, you are left with $\lambda ={\frac {hc}{E}}$ . If you know the energy of the photon, you can calculate its wavelength.^[7]

This equation can also be used to determine the maximum wavelength of light necessary to ionize metals. Simply use the energy required for ionization and solve for the corresponding wavelength.
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Plug in the known variables and solve. Once you have rearranged the equation, you can solve for the wavelength by plugging in the variables for energy. Because the other two variables are constants, they are always the same. To solve, multiply the constants together and then divide by the energy.^[8]
- For example: Find the wavelength of a photon with an energy of 2.88 x 10^-19 J.

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Check your answer by multiplying the wavelength by the frequency. If you found the right value for the wavelength, multiplying by the frequency should get you the wave speed you started with. If it doesn't, check your math. If you are using a calculator, make sure you have typed the numbers in correctly.
- For example: What is the wavelength of a 70 Hertz sound wave traveling at 343 meters per second?
  - You follow the instructions above and get an answer of 4.9 meters.
  - Check your work by calculating 4.9 meters x 70 Hz = 343 meters/second. This is the wave speed you started with, so your answer is correct.
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Use scientific notation to avoid calculator rounding errors. Wavelength calculations often involve very large numbers, especially if you're working with light speed. This can lead to rounding errors on your calculator. Prevent this by writing your numbers in scientific notation and double checking the significant digits.^[9]
- For example: Light travels through water at about 225,000,000 meters per second. If the wave's frequency is 4 x 10¹⁴ Hz, what is its wavelength?
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Do not change frequency when a wave enters a different medium. Many word problems involve a wave that crosses the boundary from one medium to another. A common mistake here is calculating a new frequency for the wave. In fact, the frequency of the wave remains the same when it crosses the boundary, while the wavelength and wave speed change.^[10]
- For example: A light wave with frequency f, speed v, and wavelength λ crosses from air to a medium with refractive index 1.5. How do these three values change?
4
Check your units. The units you use will often tell you what to do when you are solving a problem. If they do not make sense when you finish, then check to see if you used the right units.
- For example, perhaps you used Joules when you should have used Hertz, so you ended up with the incorrect answer.

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Question

What is the formula for wavelength?

Meredith Juncker is a PhD candidate in Biochemistry and Molecular Biology at Louisiana State University Health Sciences Center. Her studies are focused on proteins and neurodegenerative diseases.

Scientific Researcher

Expert Answer

Wavelength can be calculated using the following formula: wavelength = wave velocity/frequency. Wavelength usually is expressed in units of meters. The symbol for wavelength is the Greek lambda λ, so λ = v/f.
Question

How do I calculate the wave length given only the frequency?

Meredith Juncker is a PhD candidate in Biochemistry and Molecular Biology at Louisiana State University Health Sciences Center. Her studies are focused on proteins and neurodegenerative diseases.

Scientific Researcher

Expert Answer

The speed of light never changes, so v will always equal 3.0 x 10^8 m/s. This value, divided by the given frequency, will give you wavelength.
Question

If the frequency of a radio wave is 4.5GHz, what is the wavelength of the wave (velocity of light=3x10m/s)?

Meredith Juncker is a PhD candidate in Biochemistry and Molecular Biology at Louisiana State University Health Sciences Center. Her studies are focused on proteins and neurodegenerative diseases.

Scientific Researcher

Expert Answer

f = 4.5 GHz = 4.5 x 10^9 Hz (Hz = s^-1) v = 3.0 x 10^8 m/s lambda = v/f = (3.0 x 10^8 m/s) / (4.5 x 20^9 s^-1) = 0.0666 m = 66.6 um
Question

How do I calculate wavelengths?

If you want to calculate the wavelength of a wave, plug the wave's speed and frequency into the equation. Dividing speed by frequency gives you the wavelength.
Question

What is the speed of a sound wave that is 30Hz and has a wavelength of 5M?

Wavelength = 5M. Freq = 30 Hz. Speed = 5m x 30 Hz. 150 m/s is speed. See formula wavelength = speed of wave / frequency.
Question

How do I work out the maximum wavelength?

To determine the maximum wavelength of light, you simply use the energy equation. If you know the amount of energy required for the reaction, you plug it into the equation λ = hc/E.
Question

If a signal has wavelength of 2um in air, how far can the front of the wave travel during 3000 periods?

A wavelength is how long a wave (signal) travels over 1 period, so the calculation would be: 2µm * 3000, which equals 6000µm, or 6mm.
Question

A station transmits radiowaves on a frequency 600Hz. How do I calculate the wavelength of the wave?

Danoyachtcapt

Top Answerer

The frequencies given are in the audio range, but if a radio transmitter could operate in that range, you could use the following equation: Wavelength in meters = 300,000 / frequency in kHz.
Question

The wavelength of the signal from radio transmitter is 200 khz. What is the wavelength from a transmitter operating at 1000 hz and at what speed do the radio waves travel?

Danoyachtcapt

Top Answerer

The frequencies given are in the audio range, but if a radio transmitter could operate in that range, you could use the following equation: Wavelength in meters = 300,000 / frequency in khz.
Question

How do I calculate wavelength of a wave using a distance-displacement graph?

The wavelength of wave is the shortest distance that the wave begins to repeat itself, or the distance between one peak the next peak. If the distance between two peaks is 2 meters, then the wavelength is 2 meters.

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Article SummaryX

To calculate wavelength, use the formula wavelength = speed divided by frequency. Just plug in the wave's speed and frequency to solve for the wavelength. Remember to use the correct units when you're using the formula and writing your answer. If you want to learn more, like how to calculate wavelength with the energy formula, keep reading the article!

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