Wave is characterized by its repetitive motion. Suppose a toy boat is riding the waves in the wave pool, as under the boat water passes, it will move up and down in the repeated and regular fashion. Though wave travels horizontally, the boat travels vertically down and up. The cycle of wave is consisting of one complete wave, which starts at zero point, going back down to the wave trough, going up to the wave crest, and back to again zero point. Waves are having three main properties, which are wave velocity, wave length, and frequency. Wave velocity is the speed with which waves propagates in the given medium. The unit of it is meter per second.
Wavelength is defined as the distance of one frequency wave peak to the other as well as is the most commonly associated with electromagnetic spectrum. It is the distance between the two corresponding points on the adjacent waves. It is quite easy to visualize the visualize the wavelength of wave as distance from one crest of wave to the next. The calculation of wavelength is dependent upon the given information. If one knows the frequency and speed of the wave, then through the basic formula, wavelength can be calculated. If wavelength of light is required to determine, given specific energy of the photon, then energy equation is required to be used. The calculation of wavelength is easy as long as one knows the correct equation.
The frequency of wave is referred to how many times the particles of the medium vibrate when the wave passes through it. The frequency unit is Hertz or 1per second.
In an equation, the wavelength is represented by the Greek word that is lambda (λ). Depending upon the kind of wave, the measurement of the wavelength can be in centimeters, meters, or nanometers (1 m = 109 nm). Moreover, the representation of frequency is by the Greek word that is nu (ν). It is the number of waves, which passes a certain point in the specifies amount of time. Usually the measurement of frequency is in the units of waves per second or cycles per second. Single wave per second is also known as Hertz (Hz), and in the SI units is the reciprocal second (s−1).
Wavelength to Frequency Formula
The formula of wavelength to the frequency is given by following;
Speed= Frequency* Wavelength
Wavelength= (Speed of the wave)/ (Frequency of the wave)
The representation of all the quantities is by a symbol. The formula is represented symbolically as below:
C = f × λ
Below is the formula in terms of the wavelength to frequency:
- λ is wavelength of the wave under consideration expressed in units of the metre.
- C is the speed of wave in a given medium that is expressed in the terms of m/s.
- F is the total frequency of wave expressed in the Hertz terms.
How to Calculate Wavelength
It is quite easy to calculate wavelength. Following are the steps involved in the calculation of wavelength.
- The first step is calculating wavelength with the wavelength equation. For finding wavelength of wave, the speed of the wave is divided by its frequency. The formula to calculate wavelength is wavelength = Wave speed/ Frequency
- The second step is using correct units. The representation of speed can be done by using both imperial and metric units. It can be seen as kilometers per hour, miles per hour, meters per second, and others. Wavelength is always almost given in the metric units, such as meters, nanometers, millimeters, and others. Generally, frequency is expressed in Hertz (Hz) that means “per second”.
- In the third step, the known quantities are plug into the equation and then it is solved. If one wants to calculate wavelength of the wave, then it is required to plug the speed of wave and frequency of wave into the equation. The wavelength is determined by dividing speed by the frequency.
Wavelength= Wave speed/ Frequency
In the last step, equation is used for solving the frequency or speed. The equation can be rearranged and solved for the frequency or speed, if wavelength is given. For calculating speed given wavelength and frequency, v= f × λ is used. For calculating frequency given wavelength and speed, f= v/ λ is used.
Steps for Catching Mistakes
Following are the steps for catching up the mistakes:
In first step, answer needs to be checked by multiplying wavelength by frequency. If one has found right value for the wavelength, then by multiplying by frequency will get the wave speed that has been started with. In case, if it does not, then calculation needs to be double checked. If someone is using calculator, then it should be making sure that numbers are types correctly.
In the second step, scientific notation is used for avoiding the calculator rounding errors. The calculation of wavelength most often involve quite large numbers, particularly if one is working with the light speed. It may lead towards rounding errors on the calculator. It needs to be prevented by writing the numbers in the scientific notation as well as significant digits needs to be double checked.
In the third step, it is advised for not changing the frequency when wave enters different medium. There are various word problems that involve a wave, which crosses the boundary from one medium to the other. One of the most common mistakes done here is calculation of a new frequency for wave. The wave frequency remains the same, when boundary is crosses by it, while the wave speed and wavelength changes.
Lastly, units are checked. The units one sees often tells what is required to be done, when problem is required to be solved. In case, if they do not make the sense when it is finished, then it becomes important to check that whether correct units are used or not.
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