Relation Between Velocity and Wavelength

Dhristi JEE 2022-24

Velocity and Wavelength Relation

Wavelength is considered as the measure of the length of a wave cycle, which is complete entirely. The velocity of a wave is considered as the distance travelled by a particular point on the wave. Generally, if you randomly take any wave, the wavelength and velocity relation will be witnessed as proportionate. This relation is expressed by using the wave velocity formula. This formula was derived in order to explain the relation between velocity and wavelength. In this article, we will have a brief discussion regarding velocity,  wavelength and how they are related to each other. We will discuss the velocity wavelength formula for better understanding.

 

Velocity

The velocity of an object is considered as the rate of change of the position of the object with respect to a particular frame of time and reference. To some, it might sound complicated and surprising, but velocity is basically speeding up a particular object in the same direction. Velocity is considered as a vector quantity because to define velocity; one needs both the direction and magnitude of the object or the wave. The SI unit of velocity got fixed as a metre per second (m/s). If you witness a change in the direction or magnitude in the velocity of a particular object, then it is believed that the object is accelerating at a certain speed.

 

Initial and Final Velocity

Initial velocity is defined as the speed at which an object travels when an initial force is applied to the object by gravity. On the other hand, the final velocity is considered as a vector quantity because it is considered as the measure of the speed and direction of a moving object when the object has reached its maximum acceleration point.

 

Constant Velocity

The motion with a constant velocity from the initial stage is considered the simplest form of motion. Normally constant velocity gets witnessed whenever an object slides over a horizontal or low surface that has a bit of friction. For example, when a puck slides over a hockey rink.

 

Wavelength

Wavelength is considered as the property of a wave in which the total distance between two identical points of two successive waves is measured or calculated. Wavelength is denoted by the Greek letter Lambda. So, the total distance that gets calculated between the trough of one wave and the next wave is known as the wavelength.

 

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The wavelength of light is defined as the distance that exists between two successive crests or troughs of the light waves.

 

The Wavelength of Visible Light

  • The wavelength of visible light, when calculated, ranges between 400 nm to 700 nm. From here, you can also learn and know about the wavelengths of different colours that got extracted from the spectrum.

  • The spectrum of visible light is believed to have different colours which have different wavelengths.

  • The violet colour that comes out of the spectrum has the shortest wavelength, whereas the red colour has the longest wavelength.

 

Relation Between Velocity and Wavelength of Light

It is considered that for any wave when you multiply the wavelength with the frequency of the wave, it gives the velocity of the wave. This formula was given mathematically by the wave velocity formula.

 

V = f × λ

Where,

V = The velocity of the wave, which gets measured using m/s

f = The frequency of the wave which gets measured using Hz

λ = The wavelength of the wave which gets measured using m

Amplitude, frequency, wavelength and velocity are considered as characteristics of a wave. In the case of a constant frequency, the wavelength is directly proportional to the velocity. This property is derived by 

 

V ∝ λ

To explain this relation between wavelength and velocity of light, let's discuss some examples.

  • In a situation when the frequency is constant if the wavelength of a wave gets doubled, then automatically, the velocity of the wave also gets doubled. 

  • In a situation when the frequency remains constant, if the wavelength of the wave increases four times from its original position, then the velocity of the wave will also increase four times.

Hence, this is a brief explanation of velocity and wavelength relation. I hope you understand every point and concept so that it can help you in the near future.


The Most Important Characteristics of Waves are Listed Below.

  1. Amplitude: The amplitude of a wave is a measurement of how far it has moved from its resting position. On the graph below, the amplitude is depicted. In most cases, the amplitude is measured by looking at a wave graph and calculating the height of the wave from its resting point. The amplitude of a wave is a measurement of its strength or intensity. When looking at a sound wave, for example, the amplitude will indicate how loud the sound is. The amplitude of the wave affects the energy of the wave in a direct proportion.

  2. Wavelength: A wave's wavelength is the distance between two corresponding positions on back-to-back cycles. This can be calculated by measuring the distance between two wave crests or troughs. In physics, the wavelength is commonly denoted by the Greek letter lambda (λ).

  3. Period and Frequency: The frequency of a wave is the number of times it cycles each second. Hertz, or cycles per second, is the unit of frequency measurement. The lower case "f" is frequently used to signify frequency. The time between wave crests is known as the wave period. The length of the period is expressed in seconds. The upper case "T" is commonly used to indicate the period. The frequency and the period are inextricably linked. The frequency is one over the period, and the period is one over the frequency. As indicated in the formulas below, they are reciprocals of each other. T = 1/f or period = 1/frequency f = 1/T or frequency = 1/period.

  4. Speed: Wave velocity is the rate at which a wave travels. Another significant characteristic of a wave is its propagation speed. This is the rate at which the wave's disturbance moves. The speed of mechanical waves is determined by the medium through which they travel. Sound, for example, travels at a different pace in water than it does in air. The letter "v" is commonly used to denote a wave's velocity. By multiplying the frequency by the wavelength, the velocity may be computed. v = f * wavelength or velocity = frequency * wavelength

FAQs on Relation Between Velocity and Wavelength

1. Discuss the Relationship Between Wavelength, Frequency and Velocity.

According to physics theory, wavelength and frequency are inversely proportional to each other, yet velocity and wavelength are both directly proportional. Let us look at a few 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.

2. State the Difference Between Speed and Velocity.

The difference between speed and velocity is as follows:-

  • Speed is considered as the time rate at which a particular is moving along in a specific path. In contrast, velocity is the measure of the rate and direction of a particular moving object.

  • The mathematical calculation of speed is very simple. The average speed of a particular object gets calculated by dividing the distance travelled by the object by the time it took to reach the endpoint. Whereas velocity is complicated and difficult to calculate because it has different methods of calculation, it gets calculated with the knowledge we have. Average velocity is calculated by dividing change in position by change in time.

3. Explain the difference between velocity and speed.

The following is the distinction between velocity and speed:

  • The rate at which anything moves along a specified path is referred to as speed. Velocity, on the other hand, is a measurement of a moving object's speed and direction.

  • Speed is calculated mathematically in a simple manner. The average speed of an object is determined by dividing the distance traveled by the time it took to reach the destination. While velocity is complex and difficult to compute due to the various methods used, it is determined using the information we have. By dividing the change in position by the change in time, the average velocity is computed.

4. What is amplitude?

The amplitude is the largest deviation from the equilibrium of the medium. This value is equal to half of the vertical distance between the wave's crest and trough in the case of a wave in a horizontal string. The amplitude of a pressure wave in the air ("sound") equals half of the pressure difference between rarefaction and compression.

5. What is the frequency of a wave?

The number of vibration cycles per second at a given position X is the frequency v of a wave. Hertz (Hz) is the frequency unit, and 1 Hz is the reciprocal of 1 second. For example, a wave with a period of T = 0.25 s completes a full vibration cycle (peak-trough - crest) at a given position in 14 a second, resulting in four vibrations every second. As a result, the frequency is f = 4 Hz. It is clear from this example that a wave's period totally determines its frequency and vice versa. = 1 / T is the relationship between these two values.

6. Where can I find notes on the relation between velocity and wavelength?

Vedantu provides notes and questions on the relation between velocity and wavelength. Professional educators prepare the content in such a way that students can understand and remember it. It covers the relationship between velocity and wavelength, as well as amplitude, frequency, and other topics. Vedantu also offers study materials and a variety of competitive exams to students in grades 1 through 12. The contents include notes, important topics and questions, revision notes, and other material. All of these resources are available for free on Vedantu.  To use all of these resources, students must first register on the Vedantu website. You can also register through Vedantu's mobile app.

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