Relation Between Frequency and Velocity

Dhristi JEE 2022-24

Heard About Wave and Displacement Before?

Frequency is recognized as the fundamental characteristic of a wave. The definition of frequency is defined as the calculation (measurement) of the sum of waves that are passing through one point in a unit of time.


We also know what velocity is. In short, it is the rate of change of displacement. We need a brief explanation to state the term ‘velocity'—the total distance covered by a point. Within the same wave is called the velocity of the wave.


Here is the relation between velocity and frequency:


V = f × λ 


Here, 


V = velocity of the wave measure (using m/s).


f = frequency of the wave measured (using Hz).


λ = wavelength of the wave measured (using m).


Explanation on Relation Between Frequency Wavelength and Velocity

Do you know the characteristics of a wave? Wavelength, amplitude, frequency, and velocity- these four parameters are the characteristics. If a wave has a constant wavelength, you may notice the increment of velocity as well as frequency. 


These three parameters are interdependent. Scientists have published many theorems and formulas based on the relation between wavelength frequency and velocity in particle physics.


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Let’s consider some examples which are related to the relation between frequency and wavelength and velocity:

  1. When a particle is radiating a wave of constant wavelength, and the value of frequency is doubled, the radiated wave's velocity is also doubled .

  2. When you notice a wave having a constant wavelength, and its frequency is four times its wavelength, then the velocity you observe is increased by four times.


Relation Between Speed and Frequency

Frequency is the total number of occurrences of a wave traveled in space (or vacuum) per unit of time. The unit for frequency is Hertz (Hz). Some common symbols are associated with frequency such as V and f.


The SI unit is Hz. S-1 is the SI base unit. The dimension for frequency is T1. The measurement of frequency is the total occurrences obtained due to a repeating wave per second. 


The more is the period in the duration of time; the less will be the occurrences. Hence, occurrences and frequency both are reciprocal to each other.


To rectify any kind of oscillatory and vibratory phenomena, physicists use frequency at most. They use frequency to determine the calculation of mechanical vibrations, sound (audio signals), light, and radio waves


Relationship Between Amplitude and Frequency

Although there is no direct relationship between frequency and amplitude or vice versa. Individually, they can be expressed by rearranging the terms of the wave equation.


Amplitude to Frequency Formula

The wave equation can be rearranged to express amplitude in terms of frequency and other variables.


\[A = y (t) sin (2\pi ft + \phi) \]


Frequency to Amplitude Formula

The wave equation can be rearranged to describe frequency in terms of amplitude and other variables.


\[f = sin - 1(y(t)A) - \phi 2 \pi t \]


Finding the Relation Between Frequency and Time

The number of cycles per unit time – the statement is used to define many cyclical processes. Those cyclical processes are waves, oscillation, frequency, and rotation, and so on. In particle physics, many physicists apply these terms to calculate certain values.


The relation between frequency and time is helping them quite enough to determine many requisite values for the benefits. Also, you will learn about frequency in optics, acoustics, and radio chapters from physics.


Frequency is denoted by a symbol (obtained from Latin letter) i.e. f


The relation between frequency and time is equal to f = 1/T


Before the invention of unit Hertz, physicists used the unit of cycles per second (cps) for frequency. This is a traditional unit of measurement. Engineers tried to calculate the frequency using certain mechanical devices. 


Statistics Between Frequency and Period

Slower or longer waves are explained with the term ‘wave period’ (not frequency). Such waves are ocean surface waves. But waves like audio radio and light are expressed with the term ‘frequency’. These waves are faster and possess higher periods.


The table given below will show you the conversion of frequency to the period:

Frequency

1 MHz (10-3 Hz)

1 Hz (100 Hz)

1 kHz (103 Hz)

1 MHz (106 Hz)

1 GHz (109 Hz)

1 THz (1012 Hz)

Period

1 ks (103 s)

1 s (100s)

1 ms (10-3 s)

1 µs (10-6 s)

1 ns (10-9 s)

1 ps (10-12 s)


Mathematical Example: The sound produced by an object in the air has a wavelength of 20 cm. Find the object's frequency and period if the sound velocity in the air is 340 ms-1.


In this, Wave-length, γ = 20 cm = 0.2 m


Sound-velocity = 340 ms-1


Frequency, f =?


Period (time), T = ?


We know Velocity = fγ


So, f = v/γ = 340 ms-1 / 0.20 m = 1700 Hz


And T = 1/f = 1 / 1700 s-1


= 0.000588 s 


= 5.88 x 10-4 s


Conclusion

Thank you for reading this article. We hope this article on Velocity and frequency was helpful for the students. You can also access sample papers, previous year papers, revision notes, and important questions from the website.

FAQs on Relation Between Frequency and Velocity

1. Do you know the three units that stand for frequency? 

Well, in frequency, these three questions are used. These three units are written below:

  1. Cycles Per Second 

  2. Waves Per Second

  3. Vibrations Per Second 

Also, physicists use Hertz for the calculation of very specific numbers. This unit is called Hz I short. The equivalent value of 1 hertz is 1 cycle per second.

2. What are the types of major frequencies used in physics?

Four types of frequencies are very common in Physics. The table is given below:

ELF (Extremely Low Frequency)

  • Frequency: 3 kHz to 30 kHz 

  • Wavelength: 100 km to 10 km

HF (High Frequency) 

  • Frequency: 3 MHz to 30 MHz 

  • Wavelength: 100 m to 10 m

VHF (Very High Frequency)

  • Frequency: 30 MHz to 300 MHz 

  • Wavelength: 10 m to 1 m

UHF (Ultra High Frequency)

  • Frequency: 300 MHz to 3 GHz 

  • Wavelength: 1 m to 100 mm

3. What are cyclic processes which use frequency?

You can call frequency as the total number of oscillations per unit of time. Cyclic processes are rotation, oscillation, waves, and so on use frequency to determine their particular intervals. When a cyclic process is completed (from one starting point to an ending point), it is called frequency.

4. Which frequency is dangerous- 50 Hz or 60 Hz?

50 to 60 Hz frequency is used as low-frequency (AC). Both are quite sensitive. But 50 Hz frequency is dangerous in many cases.  AC current with 50 hertz sometimes may encourage calamities.

5. Explain the relation between frequency and velocity.

The link between frequency and time period is defined by the number of waves per second, and the time period is defined by the number of seconds of each wave. The relation between frequency and time period can be expressed as


\[f = 1 T f = 1T or , T = 1 f \]


A shorter time is noticed when the frequency is higher. Frequency is measured in hertz (Hz), with 1 Hz equaling one cycle or one wave per second.


The velocity of propagation, the wavelength travels one wavelength in one period, hence V is the distance the wave travels in one period. The equation form is written as


V=λT


or, V=fλ


Here, 


V is the velocity of the wave in m/s (metre per second).


f is the frequency of the wave in Hz (Hertz).


λ is the wavelength of the wave in meters.


This is the equation relating the velocity, frequency and wavelength of a wave.

We can deduce from this that in a medium with constant V, the higher the frequency, the shorter the wavelength.


For all forms of waves, this relation is true. Water waves, sound waves, and visible light are all affected by this relation. The amplitude of a wave is independent of its velocity and is solely determined by its energy.


When the frequency of a wave is doubled while its wavelength remains unchanged, the wave's velocity is also doubled.


When the frequency of a wave is four times that of its wavelength, the velocity is also four times that of the wave.

6. Derive relation between -wavelength, wave velocity and frequency.

Let the velocity of a wave be v, time period be T, frequency be n and wavelength λ.


By the definition of wavelength,


Wavelength = Distance travelled by the wave in one time period i.e., in T second


Or, wavelength = Wave velocity x Time period


Or, λ = v x T


Or, λ = v x 1/n  (As, T = 1/n)


Therefore, v =  nλ


Therefore, Wave velocity = Frequency x wavelength

7. Explain the Relationship Between Wavelength, Frequency and Velocity

According to physics theory, wavelength and frequency are inversely proportional to each other, whereas velocity and wavelength are both directly proportional. Let's look at some examples to better understand how this relationship works:


Because the wavelength is directly proportional to velocity, when the wavelength of the wave rises while the frequency remains constant, the wave's velocity also increases.


When a wave's frequency rises while its wavelength remains constant, the wave's velocity rises.


Because they are inversely proportional, the wavelength of the wave falls as the frequency of the wave increases.

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