# Wave Motion and Relation of Wavelength with Velocity and Frequency

What is Wave?

A wave is a disruption in the medium which causes the particles of the medium to undergo vibratory motion about their mean position in equal intervals of time.

Waves play an essential function in our everyday life. This is because waves are a carrier of energy and information over big distances. Waves transport energy without carrying matter. The energy transportation is carried by a disruption, which expands from a source. We are well acquainted with various kinds of waves such as water waves in the ocean, or little ripples on a still pond due to raindrops.

When a musician plucks a guitar-string, sound waves are created which on reaching our ear, produce the sensation of music. Wave disruptions might also be available in a focused package like the shock waves from an aeroplane flying at supersonic speed. Whatever might be the nature of waves, the mechanism by which it carry energy is the same.

The wave is created by an oscillation in the vibrating body and propagation of a wave through the area is using oscillations. There are 2 categories of waves:

1. Mechanical waves
2. Electromagnetic waves
##### 1. Mechanical waves

The waves which propagate by the oscillation of material particles are known as mechanical waves.

##### 2. Electromagnetic waves.

Waves which do not require any medium for their propagation are called electromagnetic waves.

For Instance: Radio waves, TV waves, X-rays, heat and light waves are some examples of electro-magnetic waves.

##### Types of Mechanical or Progressive Waves

A wave, which transfers energy by moving far from the source of disturbance, is called a progressive or traveling wave. There are two kinds of progressive waves – transverse waves and longitudinal waves.

##### Longitudinal waves

In longitudinal waves, the particles of the medium move back and forth along the direction of propagation of the wave.

Longitudinal waves can be produced on a spring (slinky) placed on a smooth floor or a long bench. Fasten one end of the slinky with stiff support and hold the other end into your hand. Now provide it a normal push and pull rapidly in the direction of its length.

A series of disruptions in the form of waves will begin moving along the length of the slinky. Such a wave includes regions called compressions, where the loops of the spring are close together, alternating with regions called rarefactions (expansions), where the loops are spaced apart.

In the regions of compression, particles of the medium are more detailed together while in the regions of rarefaction, particles of the medium are spaced apart. The range in between two consecutive compressions is called the wavelength. The compressions and rarefactions move backwards and forward along the instructions of motion of the wave.

##### Transverse waves

In transverse waves, the vibratory motion of particles of the medium is perpendicular to the direction of propagation of waves.

A big and loose spring coil (slinky spring) can be utilized to show the result of the motion of the source in generating waves in a medium. It is better that the spring is laid on a smooth table with its one end fixed so that the spring does not sag under gravity.

If the free end of the spring is vibrated from side to side, a pulse of a wave having a displacement pattern will be created which will move along the spring. If the end of the spring is returned and forth, along the direction of the spring itself, a wave with back and forth displacement will travel along with the spring. Waves in which the displacement of the spring is perpendicular to the direction of the waves are called transverse waves.

##### Relation between Velocity, Frequency and Wavelength

Wave is a disruption in a medium which travels from one place to another and for this reason, it has a specific velocity of travelling. This is called the velocity of the wave which is specified by

Velocity = distance/time

v= d/t

If the time taken by the wave in moving from one point to other is equal to its time period T, then the range covered by the wave will be equal to one wavelength, for this reason λ we can say that:

v= λ/ T

But time period T is reciprocal of the frequency f, i.e., T = 1/f.

So, v= fλ.

##### Waves as a Carrier of Energy

Energy can be moved from one place to another through waves. For instance, when we shake the stretched string up and down, we offer our muscular energy to the string. As a result, a set of waves can be seen travelling along the string. The vibrating force from the hand interrupts the particles of the string and sets them in motion. These particles then transfer their energy to the nearby particles in the string. Energy is thus moved from one location of the medium to the other in the form of a wave.

The quantity of energy brought by the wave depends on the distance of the extended string from its rest position. That is, the energy in a wave depends on the amplitude of the wave. If we shake the string faster, we offer more energy per second to produce a wave of higher frequency, and the wave delivers more energy per second to the particles of the string as it moves forward. Water waves likewise move energy from one location to another.

### MCQs

• What is a wave?
• A. A disturbance in the medium causing particles to move randomly
• B. A disruption in the medium causing particles to move periodically
• C. A transfer of matter from one place to another
• D. A stationary phenomenon in a medium

Answer: B. A disruption in the medium causing particles to move periodically

• Which of the following is NOT a type of mechanical wave?
• A. Longitudinal wave
• B. Transverse wave
• C. Electromagnetic wave
• D. Progressive wave

• In which type of wave do particles of the medium move back and forth along the direction of wave propagation?
• A. Transverse wave
• B. Electromagnetic wave
• C. Longitudinal wave
• D. Standing wave

• What is the relation between velocity (v), frequency (f), and wavelength (λ) of a wave?
• A. v = f/λ
• B. v = f + λ
• C. v = f × λ
• D. v = f – λ

Answer: C. v = f × λ

• What type of wave has vibratory motion perpendicular to the direction of propagation?
• A. Longitudinal wave
• B. Transverse wave
• C. Progressive wave
• D. Standing wave

• Which of the following waves requires a medium for propagation?
• A. Electromagnetic wave
• B. Transverse wave
• C. Longitudinal wave
• D. Standing wave

• What is the velocity of a wave if its frequency is 50 Hz and wavelength is 2 meters?
• A. 25 m/s
• B. 100 m/s
• C. 50 m/s
• D. 2.5 m/s

• Which of the following waves carries energy without carrying matter?
• A. Longitudinal wave
• B. Transverse wave
• C. Mechanical wave
• D. Electromagnetic wave

• What term is used to describe regions in a longitudinal wave where particles are spaced apart?
• A. Rarefactions
• B. Compressions
• C. Troughs
• D. Crests

• What is the time taken for one complete oscillation of a wave called?
• A. Wavelength
• B. Frequency
• C. Amplitude
• D. Time period

• Which of the following is NOT a type of progressive wave?
• A. Longitudinal wave
• B. Transverse wave
• C. Electromagnetic wave
• D. Standing wave

• What term is used to describe the distance between two consecutive compressions in a longitudinal wave?
• A. Wavelength
• B. Amplitude
• C. Frequency
• D. Time period

• What is the property of a body due to which it withstands any change in its state of rest or movement?
• A. Momentum
• B. Inertia
• C. Frequency
• D. Amplitude

• Which type of wave has a displacement pattern perpendicular to the direction of the wave?
• A. Longitudinal wave
• B. Transverse wave
• C. Progressive wave
• D. Standing wave

• What is the SI unit of frequency?
• A. Hertz
• B. Meter
• C. Newton
• D. Pascal

• What term describes the highest point of a wave?
• A. Wavelength
• B. Amplitude
• C. Frequency
• D. Crest

• Which law of wave motion states that to every action, there is an equal but opposite reaction?
• A. Newton’s First Law
• B. Newton’s Second Law
• C. Newton’s Third Law
• D. Hooke’s Law

• Which type of wave has particles moving in a direction parallel to the wave motion?
• A. Transverse wave
• B. Longitudinal wave
• C. Electromagnetic wave
• D. Progressive wave

• What phenomenon allows a wave to travel from one place to another without carrying matter?
• A. Dispersion
• B. Diffraction
• C. Refraction
• D. Energy transfer

• What is the distance between two consecutive crests or troughs of a wave called?
• A. Amplitude
• B. Frequency
• C. Wavelength
• D. Time period

Further Reading:  Self-Induction, Self-Inductance and Its Unit

### FAQs Related to Wave Motion and Wavelength:

1. What is a wave, and how does it function in everyday life?
• A wave is a disruption in a medium that causes particles to undergo vibratory motion. It serves as a carrier of energy and information over long distances without carrying matter.
2. What are the two categories of waves, and how do they differ?
• Waves are categorized into mechanical waves, which propagate through the oscillation of material particles, and electromagnetic waves, which do not require a medium for propagation.
3. What are examples of electromagnetic waves?
• Examples of electromagnetic waves include radio waves, TV waves, X-rays, heat waves, and light waves.
4. What are the two types of mechanical or progressive waves?
• Mechanical or progressive waves are classified into transverse waves and longitudinal waves.
5. How do longitudinal waves differ from transverse waves?
• In longitudinal waves, particles of the medium move back and forth along the direction of wave propagation, whereas in transverse waves, the vibratory motion of particles is perpendicular to the direction of propagation.
6. What is the relation between velocity, frequency, and wavelength of a wave?
• The velocity of a wave (v) is equal to the product of its frequency (f) and wavelength (λ), expressed as v = fλ.
7. How does a wave serve as a carrier of energy?
• Waves transport energy from one place to another by transferring the energy imparted to the medium by a disturbance. For example, when a string is shaken, the resulting waves carry energy along the string.
8. What factors determine the amount of energy carried by a wave?
• The amplitude of the wave, which is the distance of the medium’s displacement from its rest position, determines the energy carried by the wave. Higher amplitudes correspond to greater energy transfer.
9. What phenomenon allows waves to travel without carrying matter?
• Waves transfer energy without carrying matter through the mechanism of energy transfer. This phenomenon enables waves like sound and water waves to propagate over long distances.
10. How are compressions and rarefactions related to longitudinal waves?
• In longitudinal waves, compressions are regions where particles of the medium are closer together, while rarefactions are regions where particles are spaced farther apart. These regions alternate as the wave propagates.
Further Reading:  Electric Current - SI Unit, Conventional Direction of Flow & More

### Summary:

Waves, characterized by disturbances in a medium, are ubiquitous in our surroundings and serve as carriers of energy and information. They come in various forms, including mechanical waves that propagate through material particles and electromagnetic waves that do not require a medium for propagation.

Mechanical waves, such as longitudinal and transverse waves, transfer energy by moving away from the disturbance source. In longitudinal waves, particles oscillate back and forth along the direction of wave propagation, creating compressions and rarefactions. Transverse waves, on the other hand, exhibit perpendicular vibratory motion to the direction of propagation.

The relationship between velocity, frequency, and wavelength of a wave is crucial. The velocity of a wave equals the product of its frequency and wavelength. Waves also serve as carriers of energy, transferring it from one location to another. The energy carried by a wave depends on factors like its amplitude and frequency.

Understanding wave motion and its relation to wavelength, velocity, and frequency provides insights into various natural phenomena and technological applications, highlighting the fundamental role of waves in our lives.