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Wavelength is a fundamental concept in physics and is a crucial parameter in understanding various phenomena, such as light, sound, and electromagnetic waves. It refers to the distance between two consecutive points in a wave that are in phase, meaning they have the same amplitude and phase. Calculating wavelength plays a pivotal role in determining the properties of waves and can be utilized in a broad range of scientific and technological applications. In this guide, we will explore the fundamental principles behind wavelength calculations and provide step-by-step instructions on how to calculate wavelength accurately. Whether you are a student studying physics or an enthusiast keen on understanding wave properties, this tutorial will serve as a comprehensive resource to enhance your understanding of wavelength calculations.
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Wavelength is the distance between two adjacent maximum points in a wave’s oscillation and is often referred to when referring to electromagnetic waves. [1] XResearch Source Depending on the available information, the wavelength can be determined in one way or another. If we know the speed and frequency, we can apply the basic wavelength formula. If we want to calculate the wavelength of light when the characteristic energy of a photon is known, we can apply the energy formula. The correct application of the formula will make it easy to calculate the wavelength.
Steps
Calculate wavelength based on speed and frequency
- Wavelength is usually represented by the letter lamda λ{displaystyle lambda } in Greek.
- Speed is usually denoted by . v{displaystyle v} .
- Frequency is usually denoted as . f{displaystyle f} .
- λ=vf{displaystyle lambda ={frac {v}{f}}}
- Always use the same unit form when applying formulas. Often in physics, mathematical operations will be calculated using standard units of measurement.
- If the frequency is given in kilohertz (kHz) or the propagation speed of the wave is given in km/s, we need to convert these values to Hertz and m/s by multiplying the given value by 1000 ( 10 kHz = 10 000 Hz).
- Example: Find the wavelength of a wave traveling with a speed of 20 m/s and with a frequency of 5 Hz.
- Wavelength=Spreading speedFrequency{displaystyle {text{Wavelength}}={frac {text{Planning rate}}{text{Frequency}}}}
λ=vf{displaystyle lambda ={frac {v}{f}}}
λ=20m/S5Hz{displaystyle lambda ={frac {20m/s}{5Hz}}}
λ=4m{displaystyle lambda =4m}
- Wavelength=Spreading speedFrequency{displaystyle {text{Wavelength}}={frac {text{Planning rate}}{text{Frequency}}}}
- Example: Find the propagation speed of a wave with a wavelength of 450 nm with a frequency of 45 Hz. v=λf=450nsquare meter45Hz=tennm/S{displaystyle v={frac {lambda }{f}}={frac {450nm}{45Hz}}=10nm/s} .
- Example: Find the frequency of a wave with wavelength 2.5 m and propagating with speed 50 m/s. f=vλ=50square meter/S2.5square meter=20Hz{displaystyle f={frac {v}{lambda }}={frac {50m/s}{2.5m}}=20Hz} .
Calculate the wavelength knowing the photon energy
- In this type of problem, the energy of a photon is usually given.
- The above formula can also be used to calculate the maximum wavelength of light required to ionize the metal. We just need to substitute the ionization energy of the metal and calculate according to the formula to get the wavelength. [8] XResearch Sources
- Example: Find the wavelength of a photon with an energy of 2.88 x 10 -19 J.
- λ=HcE{displaystyle lambda ={frac {hc}{E}}}
= (6,626∗ten−34)(3,0∗ten8)(2,88∗ten−19){displaystyle {frac {(6,626*10^{-34})(3,0*10^{8})}{(2.88*10^{-19})}}}
=(19,878∗ten−26)(2,88∗ten−19){displaystyle ={frac {(19,878*10^{-26})}{(2.88*10^{-19})}}}
=6,90∗ten−7meters{displaystyle =6,90*10^{-7}{text{meters}}} . - Convert back to nanometers by multiplying the above result by 10 9 . The wavelength in this example in nanometers is 690 nm.
- λ=HcE{displaystyle lambda ={frac {hc}{E}}}
Proofreading
- Example: Calculate the wavelength of a 70 Hz sound wave traveling at 343 meters per second.
- After following the instructions above, you have a result of 4.9 meters.
- Double-check the calculation by calculating 4.9 meters x 70 Hz = 343 meters per second. This is also the speed of wave propagation that the problem gives, so the answer of 4.9 meters is correct.
- Example: Light travels through water at a speed of 225 000 000 meters per second. Given that the frequency of the light wave is 4 x 10 14 Hz, what is the wavelength?
- The propagation rate is written to a power of 2.25 x 10 8 . The frequency has been correctly written to the exponentiation.
- Wavelength=Spreading speedFrequency{displaystyle {text{Wavelength}}={frac {text{Planning rate}}{text{Frequency}}}}
=2,25∗ten84∗ten14=2,254∗ten6{displaystyle ={frac {2,25*10^{8}}{4*10^{14}}}={frac {2,25}{4*10^{6}}}}
=0,563∗ten−6meters{displaystyle =0.563*10^{-6}{text{meters}}}
=5,63∗ten−7meters{displaystyle =5.63*10^{-7}{text{meters}}} .
- Example: A light wave of frequency f , propagation speed v , and wavelength λ propagates from air into another medium with a refractive index of 1.5. How do the three values above change?
- The propagation speed in the new medium is equal to vfirst,5{displaystyle {frac {v}{1,5}}} .
- The frequency does not change and remains the same value as f .
- The wavelength in the new medium is New speedFrequency=vfirst,5f=vfirst,5f{displaystyle {frac {text{New Speed}}{text{Frequency}}}={frac {frac {v}{1.5}}{f}}={frac {v}{1.5f}} } .
This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
There are 8 references cited in this article that you can see at the bottom of the page.
This article has been viewed 187,890 times.
Wavelength is the distance between two adjacent maximum points in a wave’s oscillation and is often referred to when referring to electromagnetic waves. [1] XResearch Source Depending on the available information, the wavelength can be determined in one way or another. If we know the speed and frequency, we can apply the basic wavelength formula. If we want to calculate the wavelength of light when the characteristic energy of a photon is known, we can apply the energy formula. The correct application of the formula will make it easy to calculate the wavelength.
In conclusion, calculating the wavelength of a wave is an essential concept in physics and is vital in understanding various phenomena such as diffraction, interference, and the behavior of electromagnetic radiation. By using the formula λ = c/f, where λ represents wavelength, c represents the speed of light or sound, and f represents frequency, one can easily determine the wavelength of a given wave. Additionally, with the help of various techniques and tools, such as spectroscopy and the use of diffraction gratings, the wavelength of electromagnetic waves can be accurately measured, contributing to advancements in fields such as astronomy, telecommunications, and medicine. Overall, having a clear understanding of how to calculate wavelength allows scientists, engineers, and researchers to analyze and manipulate waves to further explore the mysteries of the universe and develop innovative technologies.
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