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Wave Frequency

As we know that some important terms for a wave include wave frequency, wave number, wave length, velocity etc. here we are discussing about wave frequency and its units, mathematical formula and its properties.

The frequency term can be easily explained by taking an example of coil of a slinky which is moved with completing two cycles in one second. The rate of its motion is 2 cycles/second. This rate is referred to as the wave frequency. Thus the wave frequency shows that how much the medium particles undergo in vibration when a wave is passed through that medium. It is cycles per second or waves per second or vibrations per second. It is not similar to period. 

Period refers to a particular time in which a work is completed but when it is repeatedly, and then we say that particular task is periodical manner. So the wave period is equal to time in medium’s particle completes one complete vibrational cycle. But frequency shows to how much time something is happened.

Wave Frequency

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What is Wave Frequency?

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We know that disturbance causing energy transfer from one point to another is called a wave. Let us consider a wave traveling from point. So let us count how many oscillations passes through that point in sometime time say 1 second. This is called the frequency of that wave with respect to that point. Thus in general, we can say wave frequency is the number of oscillations made by the wave per unit time. The unit for wave frequency is Hertz or Hz.

Wave Frequency Definition

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The Wave frequency is defined as "The total number of vibrations or oscillations made by the particles per unit time is called the Wave Frequency and is denoted by f.

The formula for the Wave Frequency is:f = $\frac{Number\ of\ Oscillation}{Time\ taken}$The inverse or the reciprocal of the time period is the frequency of the wave.

The frequency is the quantity obtained when we divide velocity of the wave by its wavelength.
f = $\frac{1}{T}$ where T = time period.
Frequency Waves
The figure depicts the different types of waves as classified according to their frequencies.

Formula for Frequency of a Wave

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Here are some of the formulas for wave frequency:
If the wave equation is
y = A sin ($\omega$ t + $\phi$)

where $\omega$ = Angular frequency,
$\phi$ = phase difference,
t = time period.

The frequency is related to angular frequency by the formula:
f = $\frac{\omega}{2 \pi}$

The formula for the frequency to the time period in a wave is:
f = $\frac{1}{T}$

where T = time period

Angular frequency,
$\omega$ = 2 $\pi$ f = $\frac{d\theta}{dt}$

Unit : Radian Per Second.

Velocity of the wave is related to the frequency by the formula:
f = $\frac{v}{\lambda}$

where f = frequency,
$\lambda$ = Wavelength.

if we consider the wave (electromagnetic wave) to be moving through vacuum then v = c or the speed of light. Hence the formula reduces to:
f = $\frac{C}{\lambda}$
Here C = 3 $\times$108 m/s.

The Frequency of a Wave is?

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The total number of vibrational cycle or the oscillations that are made per second by the particles is called frequency of the wave. or The total number of distinct cycles that are completed in unit time.

The frequency is dependent on both wavelength and velocity of the wave. The mathematical relation to wavelength and velocity by the following formula: 
V = f $\lambda$
where V = Velocity of the wave,
f = frequency of the wave,
$\lambda$ = wavelength of the wave.

The Frequency of a Sound Wave Determines?

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The total number of complete back-and-forth particle vibrations of the medium per unit time in sound wave is called the Sound Wave Frequency.
For the sound wave we use Hertz as the unit of measurement where 1 Hertz = 1 vibration/second.

Conceptually whenever a wave passes the medium it makes the first particle to which it comes in contact, vibrate. Then this particle vibrates the nearby particle at the same frequency. This is how energy is propagated. This is clear that the particles vibrate at the same frequency.
Waves can be of two types:
  1. High frequency wave
  2. Low frequency wave.
In a High frequency wave the numbers of vibrations per unit time are far more than that of a low frequency wave.
The sound moreover depends on pitch, loudness and quality where pitch is related to frequency of the sound wave.

Radio Waves Frequency

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  1. These are the waves which are having the lowest frequency in the electromagnetic spectrum. They are given out by transmitter.
  2. They are formed as a result of thunder, lightning etc.
  3. They are used in communication mostly.
  4. They are of four types of radio waves namely: 
    • Long wave
    • Medium wave
    • Ultra high frequency (UHF)
    • Very High frequency (VHF).
The Prolonged exposure to these frequency rays is known to cause cancer.


They are Used by antennas.
They are used for data transmission via modulation.
The frequency ranges from 3 KHZ to 3000 GHz. This is also called radio frequency.

High Frequency Waves

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The High frequency waves are the waves with extremely less wave length.They have a high frequency. Hence they pass through a given point many number of times every second. These are utilized in communication over long distances. Ultrasonic waves and gamma waves are the examples of such waves. Greater the frequency greater would be the pitch.

They can be used for communication to moon.
They Can also be used for various other scientific functions and research.

Sine Wave Frequency

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Sine wave is a mathematical function. It basically tells us about the smooth oscillation that is repetitive.
The sine wave is expressed as:
y = A sin ($\omega$ t + $\phi$)
Here A = amplitude of the sine wave
$\Phi$ = phase of the wave
$\omega$ = angular frequency of the wave
Also $\omega$ = 2 $\pi$ f
Here f is the frequency of the wave.

How to Calculate Frequency?

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Using above formulas we can calculate the frequency. Below are given some problems on frequency:

Solved Examples

Question 1: Frequency of a wave motion is 250 Hz. what is its time period?
Frequency f = 250 Hz.
Time period T = $\frac{1}{f}$
                    = $\frac{1}{250 Hz}$
                    = 0.004s.

Question 2: What is the frequency of a wave with a time period of 0.05 seconds?
given Time period, T = 0.05 s
The Frequency is given by
f = $\frac{1}{T}$
f = $\frac{1}{0.05 s}$
  = 20 Hertz.
Frequency, f = 20 Hertz.

Question 3: A Sound wave traveling in air has a wavelength of 1.6 $\times$ 10-2 m. if the Velocity of sound is 320 m/s. Calculate the frequency of the sound?
Wavelength of the sound $\lambda$ = 1.6 $\times$ 10-2 m,
Velocity of sound (V) = 320 m/s
Velocity of sound is given by V = f $\lambda$.
Frequency f = $\frac{V}{\lambda}$
                  = $\frac{320 m/s}{1.6 \times 10^{-2} m}$
                  = $\frac{320 \times 10^{3}}{16 s}$
                  = 20 $\times 10^{3}$ Hz
Frequency f = 2 $\times 10^{4}$ Hz.

The Apparent change in frequency or wavelength observed by the observer when there is a relative motion between the source and the observer is known as Doppler Effect.

Doppler effect takes place both in sound as well as light. If sound is considered it totally depends if the source or observer or both are in motion, while if in light it is dependent only on the fact that whether the distance between source and observer is decreasing or increasing.

Doppler Effect

Conditions when Doppler Effect is observed for sound waves:
  1. When the source of sound is in motion and the observer at rest.
  2. When the observer is in motion and the source at rest.
  3. When the source and the observer are moving with unequal velocities.
  4. When the source and the observer and intervening medium are in motion.
Conditions when it is not observed in sound waves:
  1. When the source of sound and the observer both are at rest then Doppler effect is not observed.
  2. When the source and the observer both are moving with same velocity in same direction.
  3. When the source and the observer are moving mutually in perpendicular direction.
  4. When the medium only is moving.
  5. When the distance between the source and the observer is constant.
  6. When source is in motion and observer is at rest then the cause of apparent change in frequency is that the waves either contract or expand.
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More topics in Wave Frequency
Doppler Effect
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