How to Find the Frequency of a Wave: Formula, Problems, Examples and Facts

How to find the frequency of a wave? The process is simple; the number of turns a particular thing takes to complete is termed to be frequency.

When an object goes around in motion, we usually determine the motion, force, and so many other factors. But we also need to know at what frequency it will travel at a given time. So the reciprocal time is given as frequency in standard terms.

In a detailed case, we also might be able to determine the frequency of a given wave, a particle in short terms and also a larger context. Frequency is a broadly used factor in terms of the wave. Say, for instance, the wave travels at a particular speed, and we are to find the frequency of the wave.

Usually, we dive into the mathematical part of the solving, but in simple terms, we also can determine waves quickly. The frequency is how many cycles it does for one second. So if a wave completes one cycle, the frequency is half of it.

Frequency is something that appears continuously or at a particular given time. Similar to the solenoid, it has a number of turn in it when wound around a conductor, and it produces electricity. In the same way, the frequency is the number of cycles a wave makes in one second, and it is usually equal to 2 hertz.

The number of cycles the light wave has made in one second is also evaluated in terms of wavelength and velocity of the light wave. The sound wave is the most common area where the frequency term is often considered.

There is also a scientific thing that is, dogs and birds get to hear the sound beyond a particular level that even human beings are not capable of hearing. We are made in such a way that only a certain amount of frequency of sound we could bear to hear.

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Frequency of a wave formula

Frequency has a general formula that can be applied to use in all contexts. The time period is the main reason that aids in the formula of frequency. 

The number of cycles a wave makes in one is regarded as the frequency of that particular wave. Therefore the formula for frequency in everyday terms is f=1/T. Here T is the time period at which the waves make the number of cycles.

In order to calculate the frequency, we need to know the specifications of a wave. A wave is a collection of vibrations termed to be energies. They have peaked on both ends. The top node is called the trough, and the bottom node is called the crest.

The height of the wave is generally regarded to be the amplitude of the wave. The height of the wave will determine whether the amplitude is larger or smaller. So when these alter, the cycles made per second also will be altered.

So when the wave completes one cycle, that is, if the wave has both crest and trough in the same phase, then the frequency made is half.

The wave completes a number of cycles in one second, and that is basically known as the frequency of the wave. And this is given the formula f=1/T. The type of wave can depend on the medium through which it is passing.

How to find the frequency of a wave from a graph?

Now let us see how to find the frequency of a wave in a graph. First, the frequency is the number of cycles the wave has attempted in order to complete one full circle at a given particular time.

When the wave makes one cycle, it will take some time to do so. In the graph, we call it units. Basically, there are a number of units in a graph from which we can quickly determine how to find the frequency of a wave in that particular case.

Say, for example, a wave travels at a particular speed, and we must as well know how many seconds it takes. Say there are 12 seconds marked on a graph, so this wave takes 4 seconds to complete one entire cycle. So, according to the formula f=1/T, the frequency of the wave is 0.25Hertz.

Let us see a few problems on the frequency calculation.

Problem:

A typical wave completes two cycles in 30 seconds, and what will be the frequency of the wave if it travels in the same medium?

Solution:

f=1/T

f=2/30

f=0.0667 Hertz

There is always confusion between the frequency of a wave and the velocity of a wave. There is the amplitude of the wave, which is basically the height of the wave. So the velocity is calculated in order to find the scalar part of the velocity which is the speed.

When we find the wave to be a light wave, sound wave or an electromagnetic wave, we need to find the frequency of the wave completing the cycles. The time period between the cycles made by the wave is usually given by the formula as the reciprocal of the frequency.

How to find the frequency of a wave with wavelength and amplitude?

How to find the frequency of a wave with wavelength and amplitude? When we consider the wave to be a light, we must know all the factors that affect the frequency of the wave.

Firstly the wavelength of the wave must be taken into consideration. How to find the frequency of a wave with the wavelength? The formula is as simple as that, and we need to find the velocity of the light formula. 

There will be a formula called the velocity of light, c = fλ. Here c is the velocity of light, f is the frequency to be determined, and λ is the wavelength of light. From this formula, we can find the frequency of the wave in terms of wavelength by rearranging the terms given in the formula. 

If a wave is said to travel at a particular speed and time, we also need to find the frequency with which the light wave is travelling. So the formula mentioned above will be used to calculate the frequency at a given time period.

Let us find the frequency of the wave and see how the frequency is determined using the formula.

Problem:

A light wave travels with a velocity of 3×108 m/s. The given wavelength of the light wave is said to be 2000 Å. What is the frequency?

Solution:

c = fλ

f= c/λ

f= 3×108 / 2000 Å

f= 1.5 x1018 Hertz

So from the above problem is evident that the frequency can be found using wavelength.

Now we need to know how to find the frequency of a wave in terms of amplitude. For this, we shall now consider the general formula of frequency, that is, f=1/T. Here f can also be written as f= ω / 2 π

Here the formula for T is given as 2 π/ ω. From this, the amplitude value is easily found if the time period is mentioned. And the frequency can be found from the above formula if the amplitude is given in the particular problem.

How to find the frequency of a wave with only the wavelength?

We need to know how wavelength affects the wave when it travels at a particular speed and in a given direction. It is how far the wave will be able to travel in a medium.

We all know the velocity of light is a standard for most formulas, and we also know how to rearrange the given formula details in order to find the frequency of a given wave. Generally, when a light wave is travelling at a particular direction with a speed of 3×108, it will also gather information about the frequency of the wave as well.

The velocity of the light formula is the base in order to find the wavelength or the frequency of the light wave that is travelling in. The velocity of the light formula is given by c = fλ. From this, we get the frequency of the wave in terms of wavelength by rearranging the formula accordingly.

The final formula is f= c/λ. Let us see a problem as to how the formula works for an electromagnetic wave.

Problem:

Calculate the frequency of an electromagnetic wave that travels at the speed of 2×106m/s having a wavelength of 1000 Å. With the given details, use the formula of the frequency in terms of wavelength.

Solution:

c = fλ

f= c/λ

f= 0.002 x 106 Hertz

f= 2 x 106/ 1000 Å

In this way, we can quickly determine the frequency of a wave using the velocity value and mainly the wavelength value.

The wavelength of a wave is basically the space between the crests or troughs of a wave that are successive. Mainly the ends of the same wave that has been transmitted in terms of sound or electromagnetic wave.

When the crests and troughs of a wave that are in the same phase points meeting each other at the exact location are generally regarded to be the wavelength of a wave.

How to find the frequency of a wave when given the period?

How to find the frequency of a wave in terms of the time period? The answer to this is straightforward as it is the general formula to find the frequency of a wave.

We must know that the time period in a wave is the distance between a crest and a trough in the same phase. So when a wave basically travels with a particular frequency in a given space of time, we need the formula to calculate the frequency. 

Here goes the formula for frequency in terms of the time period, f=1/T. The time period is generally another term for the amplitude of the wave. T can also be written as 2 π/ ω, where the ω is the measure of amplitude. 

The amplitude is basically the height of a wave depending on which we need to conclude the amplitude being large or small. If the height of the wave is high, then the amplitude is said to be significant, and if the height of the wave is small, then the amplitude of the wave is said to be small.

The amplitude has two ends, named crest and trough. The trough is the top node of the amplitude, and the crest is the down node of the amplitude.

When the distance between two waves is named as wavelength, and the number of cycles one wave makes is termed as the frequency when the times period is one unit on the graph, which is basically one second in standard terms.

How to find the frequency of a wave without the speed?

From the formula of the velocity of light, we might have noticed that the wavelength of a wave is inversely proportional to the frequency of the wave, that is, the cycles made by the wave in a time period.

We also know that the frequency is not directly proportional to the time period; hence, wavelength and time period are proportional to each other. Wavelength is connected to energy, so when the wavelength increases, the energy decreases. The formula is from the energy of a photon. 

We assume the wavelength and time period to be proportional and the frequency and energy to be proportional. The frequency of a wave without the speed would be the energy formula where E=hf, where E is the energy, h is the plank’s constant and f is the frequency.

So knowing the specific basic formula of light and energy, we can rearrange the terms accordingly and know how to find the frequency of a wave in all terms possible. Also, all these factors affect the wave and its quantities in aid to its own propagation.

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