Waves, parameters, types of waves and their properties, practice problems, FAQs

As we know that sounds propagate through waves, also food can be cooked in the oven by the EM waves. So, can we cook the food just by playing a sound speaker? This is not possible. But why? Although both are waves and propagate the energy, both have different properties so different uses. Sound wave is a mechanical wave and the wave used in the oven is a microwave which is an electromagnetic wave. Similarly we have different kinds of waves which have their different properties and uses. Let's see the different types of waves !

Table of content

• What are waves?
• Wave parameters
• Types of waves
• Mechanical waves
• Electromagnetic waves
• Matter wave
• 1 D, 2 D, 3 D wave
• Practice problems
• FAQs

What are waves?

Wave is a propagation of energy and momentum with or without the use of a medium from one place to another place. The energy can propagate in any form of the elastic deformation of a particle of medium, variation in pressure, electric and magnetic field intensity etc. We can represent a wave as shown in the figure.

Wave parameters

• The maximum displacement of oscillation is called the amplitude of the wave.
• The distance between two consecutive maximas is called wavelength of wave.
• The time to complete one oscillation is called the time period (T) of oscillation.
• The number of oscillations in one second is called the frequency of waves. Unit of frequency is Hz .The frequency can be related with time period as

$Frequency=\frac{1}{Time period}$

Now let's discuss the types of waves.

Types of waves

We have to deal with various waves in our daily life such as string waves, sound waves, radio waves etc., based on the medium waves can be classified as -

• Mechanical waves
• Electromagnetic waves
• Matter waves

Based on the particle motion waves can be classified as

• Transverse waves
• Longitudinal waves

Based on the propagation in space waves can be classified as

• 1 D wave
• 2 D wave
• 3 D wave

Mechanical waves

A wave that needs a medium to propagate is called a mechanical wave. The medium has the elastic and inertial properties. When a disturbance is produced in the medium due to inertial and elastic properties of the medium, this disturbance propagates in the medium.

• Example of mechanical wave

Examples of mechanical waves are as follows :

• Wave in a stretched string
• Sound wave
• Tsunami waves
• Wave in oscillation of spring

• Properties of the mechanical waves

• In mechanical waves the energy and momentum transfer through the medium.
• The particles of the medium do not move with the wave but oscillate about their mean position.
• As mechanical waves need a medium having inertial and elastic properties, they cannot move in the medium.

• Types of mechanical waves

The mechanical wave further can be classified into two parts as transverse and longitudinal waves.

1. Transverse waves - Transverse waves are defined as waves in which the particle of the medium oscillates perpendicular to the direction of the wave motion. The point about which the particle oscillates is called the mean position. The uppermost point is called crest of the wave and lowest point is called trough of the wave. Wave on string, S-type earthquake waves, and the motion of spring in the figure are the examples of transverse waves.

2. Longitudinal wave - Longitudinal waves are defined as the wave in which the particles of the medium oscillate parallel to the direction of the wave motion. The longitudinal wave travels in the forms of compression and rarefaction. When the particles of the medium come closer, then it is called compression. When the particles of the medium move apart, then it is called rarefaction. Sound waves, p-type earthquake wave, motion of spring in the figure below are examples.

Electromagnetic waves

In an electromagnetic wave the electric field and magnetic field oscillate perpendicular to the direction of wave motion. Magnetic field and electric field are mutually perpendicular.

• Examples where electromagnetic wave is involved

The examples where electromagnetic waves are involved are as follows-

• Radio and television
• Microwaves oven
• Radar

• Properties of electromagnetic waves

• Medium is not required for electromagnetic waves.
• They can propagate in the vacuum with the speed of light.
• Electromagnetic waves are transverse in nature and can be polarized.
• Electromagnetic waves perform interference and diffraction.

• Types of electromagnetic waves

In the increasing order of the wavelength the electromagnetic waves are

1. Gamma rays : Gamma rays have the wavelength of order 10^-11 m . Used in the medical field. It kills cancer cells.
2. X- rays : X- rays have the wavelength of order 10^-9 m and used to see the inner body part.
3. Ultraviolet : have the wavelength of order 10^-7 m , used in fluorescent tubes. Ultraviolet rays coming from the sun are harmful for the skin.
4. Visible light : Visible light has the wavelength of order 510^-6 m. It helps in seeing objects of different colors.
5. Infrared : have the wavelength of order 10^-5 m. Transfer of heat from sun, fire and radiators.
6. Microwave : have the wavelength of order 10^-3 m . Used in cooking, radar, telephone and other signals.
7. Radio waves : Radio waves have the wavelength of order 10¹ m, it is used to broadcast the radio and television.

Matter wave

A french physicist De broglie gave the concept of the dual nature of matter. According to which, when a matter particle moves with a larger velocity it behaves as a wave.The wavelength of matter wave is called de broglie wavelength, and is given by

$\lambda =\frac{h}{p}=\frac{h}{mv}$

Where h= planck’s constant = 6.62 × 10^-34m² kg/s

p = momentum of particle
m = mass of particle
v = velocity of particle

However it is difficult to observe this phenomena in day-to -day life. But it can be seen in various physical experiments like, a beam of electrons shows diffraction just like the beam of light which is an electromagnetic wave.

1D, 2D, 3D wave

1. 1-Dimensional wave : Wave on string is an example of a 1-Dimensional wave.

2. 2-Dimensional wave : Water wave is an example of a 2-Dimensional wave.

3. 3-Dimensional wave : Sound Wave is an example of a 3-Dimensional wave.

Practice problems

Q1. What is the wavelength of a wave shown in the figure ?

A. In figure the 2 waves having the length 12 m

Hence _{$$\begin{gathered} 2\lambda =12 m \\ \lambda =6 m \end{gathered}$$}

Hence wavelength of the wave is 6 m

Q2. The time period of a wave is 0.2 s, then what is the frequency of the wave?

A. Given the time period of wave is T=0.2 s

We know the relation of frequency with time period

$$\begin{gathered} Frequency=\frac{1}{Time period} \\ Frequency=\frac{1}{0.2} \\ Frequency=5 Hz \end{gathered}$$

Q3. An electron is moving with the velocity 1.6 $\times$ 10⁶ m/s, find the wavelength associated with electrons. Mass of an electron is 9.1 $\times$ 10^-31 and planck’s constant is 6.62 × 10^-34m² kg/s .

A. Given Planck’s constant h = 6.62 × 10^-34m² kg / s
Mass of the electron m=9.1×10^-31
Velocity of electron v=1.6×10⁶ m/s
The wavelength of a matter wave is given by

$$\begin{gathered} \lambda =\frac{h}{mv} \\ \lambda =\frac{6.62 \times {10}^{-34}}{(9.1\times {10}^{-31})(1.6\times {10}^6)} \\ \lambda =4.55\times {10}^{-10} \end{gathered}$$

=6.62× 10-34(9.110-31)(1.6106)

=4.5510-10

Q4. Write the difference between the transverse waves and longitudinal waves.

A. We can differentiate the transverse waves and longitudinal waves as

FAQs

Q1. Velocity of a mechanical wave depends on?

A. Properties of the medium of propagation define the velocity of a wave.

Q2. Which type of wave is a Sound wave?

A. Sound wave is a longitudinal wave.

Q3. On what factor does the frequency of waves depend?

A. Frequency of wave depends on the source of the wave.

Q4. What are the different colors of visible light?

A. In the increased order of wavelength, the colors are Violet, Indigo, Blue, Green, Yellow, Orange, Red.