Lecture-7: Chapter-2 (Waves & Oscillation)

General wave properties

Wave:  Wave is a form of disturbance which travels through the elastic medium  due to the repeated periodic motion of the particles of the medium. For example, when we drop a pebble into a pond of still water, a few circular ripples (disturbances) move outwards on the surface of the water. As these circular ripples spread out, energy is being carried with them.

Source of waves: The source of any wave is a vibration or oscillation. For example, we can produce waves on a rope by fixing one end to a wall and moving the other end up and down as shown in Fig-2. The up and down movements make up the vibrations and oscillations.

Types of waves:There are two main types of waves. They are

1.   Mechanical waves and 2. electromagnetic waves

Mechanical waves: These waves propagate through a medium, and the substance of this medium is deformed. The deformation reverses itself owing to restoring forces resulting from its deformation.     For example, sound waves propagate via air molecules colliding with their neighbors. When air molecules collide, they also bounce away from each other (a restoring force). This keeps the molecules from continuing to travel in the direction of the wave.

Electromagnetic (EM) waves: These waves do not require a medium. Instead, they consist of periodic oscillations in electrical and magnetic fields generated by charged particles, and can therefore travel through a vacuum. These types of waves vary in wavelength, and include radio waves, microwave, infrared radiation, visible light, ultraviolet radiation, X-rays, and gamma rays. Fig. below shows the EM spectrum with increasing wavelength.

Gamma ray

X-ray

Ultraviolet radiation

Visible light

Infra-red radiation

Microwave

Radio wave

Some common properties of all EM wave:

1.   They are all transverse waves.

2.   They travel at the same speed of light 3X10⁸ m/s in vacuum.

3.   They do not require any material medium to travel.

4.   They obey the laws of reflection, refraction and diffraction.

5.   They can be emitted and absorbed by matter.

6. The wave equation v=f λ is applicable to all these waves.

Waves are classified into another two types depending on the direction of its oscillation. They are:              1. Transverse wave and 2. Longitudinal wave               
1. Transverse wave: The wave in which vibration of particles are perpendicular (at right angles) to the direction of wave propagation (the direction of energy transfer) are called transverse wave.            Examples: Water wave, light wave and all EM waves.

 
2. Longitudinal wave: The wave in which vibration of particles are parallel to the direction of wave propagation (the direction of energy transfer) are called longitudinal wave.                                    Examples: Sound wave and wave in a spring.

Wave parameters:

1.   Crests and troughs: These are the high points and low points that characterize transverse wave only. For longitudinal waves, the terms are compressions and rarefactions.

2.   Amplitude, A: It is the maximum displacement fron the rest or central position, in either direction. Its SI unit is meter (m).

3.   Frequency, f: It is the number of complete waves made in one second. It’s SI unit is cycle/second or Hertz (Hz).

4.   Wavelength, λ: It is the distance between two point on a wave that are in phase or it is the distance between two crests or troughs. Its SI unit is meter (m).

5.   Period, T: It is the time taken to produce one complete wave. Its SI unit is second (s).

6.    Wave speed, v: It is the distance traveled by a wave in one second. Its SI unit is meter/second (m/s).

·       The relation between frequency and time period:

T=1/f

·       The relation between frequency, wavelength and speed:

V=f λ

Example-1: A wave is moving on a slinky with a frequency 3 Hz and a wavelength of 0.3 m. What is the wave speed?

Solution: Given: f= 3 Hz, λ=0.3 m, v=?

We know, v= f λ or, v= 3X0.3=0.9 m/s (Answer).

Example-2: The speed of green light of wavelength 0.6 μm in vacuum is 3.0X10⁸ m/s. What is its frequency?

Solution: Given: v= 3X10⁸ m/s, λ=0.6 μm= 0.6X10^-6 m, v=?

We know, v= f λ or, f=v/ λ =3X10⁸ / 0.6X10^-6 =5.0X10¹⁴ Hz (Answer).

Distinction between transverse and longitudinal wave

Sl. No.	Transverse wave	Longitudinal wave
1	The wave in which vibration of particles are perpendicular (at right angles) to the direction of wave propagation (the direction of energy transfer) are called transverse wave.	The wave in which vibration of particles are parallel to the direction of wave propagation (the direction of energy transfer) are called longitudinal wave.
2	During propagation of the wave crests and troughs are produced in the medium.	During propagation of the wave compression and rarefaction are produced in the medium.
3	The distance between two successive crests or troughs is called wavelength.	The distance between two successive compressions or rarefaction is called wavelength.
4	Polarization of the medium takes places.	Polarization of the medium does not takes places.