Relation between Velocity and Wavelength

Waves are the patterns of movement that happen without any flow or transfer of physical matter but the disturbance is also created for example when we speak, we emit sound energy in the form of waves which does not create any big difference in the outside environment still the ears or microphone can catch the sound signals and decode it and hear. Wavelength is the measurement of the length of one complete wave cycle. The velocity of a particular wave is the distance covered by the point on the wave. In most waves, the wavelength of the wave is directly proportional to its velocity. The wave velocity formula is used to derive the proportional relation between the wavelength and velocity. In this article, we will look at the wavelength, velocity, and the relationship between the two.

Keyterms: Waves, Velocity, Wavelength, Lambda, Light, VIBGYOR, Magnitude, Motion, Speed, Length, Meter, Acceleration

---

Wavelength

The wavelength of the wave is the minimum distance between the two points on one wave in the same phase. Wavelength is represented by λ(lambda). It can also be defined as the distance between the two consecutive crests or troughs of the same wave in the same phase. The wavelength of any particular wave is called its property, the wavelength of the wave decreases with time or is changed when it is passed from one medium to another. The frequency of the wave, however, doesn’t depend on its medium and stays unchanged when passed from one medium to another.

Wavelength

The wavelength of the light is the distance between the crests or troughs of the waves of the light waves. The wavelength of the light(visible) ranges between 400nm to 700nm, the wavelengths of the lights of different colors (extracted from a spectrum) are also not the same. VIBGYOR is extracted from the spectrum in which different colors are placed in increasing order of their separated respective wavelengths. According to this information, we can conclude that the violet-colored light has the minimum value of the wavelength whereas the red light has the maximum value for its wavelength. Or violet light has the shortest wavelength and red light has the longest wavelength.

Spectrum of Light

---

Velocity

The velocity of any object is the rate of change of its position with time and with respect to the reference point. The velocity of any object is a vector quantity, the vector quantities are the quantities with magnitude (numerical value) and direction. Quantities with only magnitude and no direction are called scalar quantities. The SI unit of velocity is meters per second (m/s). 

Velocity

Initial velocity: initial velocity of the object or wave is considered as the velocity of wave or object at the starting time when the observation is done. If we see only the magnitude of the initial observation time, then it is known as the initial speed of the object or the wave.

Final velocity: The final velocity of any object or wave is the velocity of the object or wave in the final time of observation, if the value of final velocity and the initial velocity is the same then the wave or object is said to be moving in constant velocity with zero acceleration or retardation also without any change in the direction of the movement. The final velocity with its direction is called its final speed.

Constant velocity: When the motion of the object is with the same speed and in the same direction then the velocity of the object or wave is unchanged and is called constant velocity. 

---

Relation between Velocity and Wavelength

For any particular wave, the velocity of the wave is calculated by multiplying the wavelength with the frequency of the wave. This formula is known as the wave velocity formula and is represented as; 

V = f × λ  

Where V is the velocity of the wave and its SI unit of measurement is m/s (meter per second),

f is the frequency of the wave the SI unit of frequency is Hertz (HZ). 

λ is the wave’s wavelength and is calculated in meters (SI unit of length).

Relation between Velocity and Wavelength

The terms – wavelength, velocity, frequency, amplitude are known as the significant characteristic properties of a wave. When the frequency of a wave is constant then the wavelength of the wave is directly proportional to the velocity of the wave. That is the wavelength of the wave increases with an increase in its velocity and wavelength decreases with a decrease in the velocity of the wave. 

Below are the two situations that can help us to understand the relation between the wavelength and velocity of the wave: -

• Let’s take a wave under the observation with a constant value of frequency, if the wavelength of the wave gets doubled then the velocity of the wave increases by two times automatically which proves that the wavelength is proportional to the velocity of the wave.
• In another situation also, the frequency is set as constant and this time the wavelength of the wave is increased by three times which will automatically result in the increase of the velocity with the same fraction. 

---

Things to remember

• Waves are the patterns of movement that happen without any flow or transfer of physical matter but disturbance. Examples of waves are light waves and sound waves
• Wavelength is the measurement of the length of one complete wave cycle. That is crest to crest or trough to trough.
• The velocity of any object is the rate of change of its position with time and with respect to the reference point.
• The white light is formed of 7 different lights that are extracted through the spectrum
• Spectrum extracts the different colored lights namely the VIBGYOR.
• The violet light has the minimum wavelength and the red light has the maximum wavelength.
• The velocity of any object is a vector quantity and has both magnitude and direction.
• When the motion of the object is with the same speed and in the same direction then the velocity of the object or wave is called to be constant velocity.
• When the frequency of a wave is constant then the wavelength of the wave is directly proportional to the velocity of the wave.

---