Production and Propagation of Waves – SS2 Physics Lesson Note (Second Term)

A wave is a disturbance that travels through a medium and transfers energy from one point to another without any permanent displacement of the medium. Wave motion is the process of transferring that disturbance without any transfer of the particles of the medium. Waves are classified by the medium they travel through and by the direction of vibration.

Behavioural objectives

By the end of the lesson, students should be able to:

• define a wave and wave motion;
• distinguish between mechanical and electromagnetic waves, and give examples of each;
• distinguish between transverse and longitudinal waves, and between progressive and standing waves;
• define phase, cycle, amplitude, period, frequency, wavelength and wave velocity;
• use the relationships f = 1/T and v = fλ to solve problems.

What are the types of waves?

Waves are classified in two ways:

1. Based on the medium of propagation: mechanical wave and electromagnetic wave.
2. Based on the comparison of the wave direction with the direction of vibration of the particle: transverse wave and longitudinal wave.

How are waves produced and propagated, based on the medium?

Mechanical waves

A mechanical wave is a wave that requires a material medium for its mode of propagation (or for it to transfer energy away from the source). Examples are waves travelling through springs, water waves and sound waves.

Electromagnetic waves

Electromagnetic waves are waves that do not need a material medium for their mode of propagation (or for them to transfer energy away from the source). Examples are radio waves, visible light, ultraviolet rays, x-rays and gamma rays. Electromagnetic waves travel at the speed of light (3.0 × 10⁸ m/s).

Progressive waves

A wave which travels along a medium transferring energy from one part of the medium to another is called a progressive wave. The progressive wave can be divided into transverse and longitudinal waves.

Progressive or travelling wave

Standing waves

A standing or stationary wave is formed when two waves travelling in opposite directions meet, or by the superimposition of an incident wave and its reflection. The amplitude of the standing wave varies along the wave.

Standing or stationary wave

How are waves produced and propagated, based on the direction of vibration?

Transverse waves

A transverse wave is a wave which travels perpendicularly to the direction of the vibrations producing the waves.

Longitudinal waves

Longitudinal waves are waves which travel in a direction parallel to the vibrations of the medium.

What terms are used in describing waves?

1. Phase: particles which have the same displacement from their positions of rest and are moving in the same direction are said to be in phase.
2. Cycle: a complete to-and-fro movement or oscillation of a vibrating particle.
3. Amplitude (A): the maximum displacement of a particle from its rest or mean position. It is measured in metres (m).
4. Period (T): the time required for a particle to perform one complete cycle or oscillation. It is measured in seconds (s).
5. Frequency (f): the number of complete cycles made in one second. It is measured in hertz (Hz).
6. Wavelength (λ): the distance covered by the wave after one complete oscillation. For transverse waves, it is the distance between successive crests or troughs. For longitudinal waves, it is the distance between successive compressions or rarefactions. It is measured in metres (m).
7. Wave velocity (v): the distance travelled by the wave in one second. The S.I. unit is m/s.

What is the relationship between wave velocity, frequency and wavelength?

Period and frequency are related by:

• f = 1/T (equation 1)
• T = 1/f (equation 2)

Wave velocity is the distance travelled by the wave divided by the corresponding time taken. For one complete oscillation, the distance is one wavelength (λ) and the time is one period (T), so:

• v = λ/T

From equation 1, f = 1/T. Substituting gives:

• v = fλ
• λ = vT

Where v = wave velocity (m/s), f = frequency (Hz), λ = wavelength (m) and T = period (s).

Worked example

A radio station broadcasts at a frequency of 300 kHz. If the speed of the wave is 3 × 10⁸ m/s, calculate the period and wavelength of the wave.

f = 300 kHz = 300 000 Hz = 3 × 10⁵ Hz

T = 1/f = 1/(3 × 10⁵) = 3.3 × 10^-6 s

v = fλ, so λ = v/f

λ = (3 × 10⁸)/(3 × 10⁵) = 1000 m

Evaluation

1. Distinguish between a mechanical wave and an electromagnetic wave, and give two examples of each.
2. Distinguish between a transverse wave and a longitudinal wave.
3. What is the difference between a progressive wave and a standing wave?
4. Define period and frequency, and state the relationship between them.
5. State the equation that links wave velocity, frequency and wavelength.

Assignment

1. (a) What is wave motion?
   (b) The equation represents a wave train in which y is the vertical displacement of a particle at a distance x from the origin in the medium through which the wave travels. Explain, with the aid of a diagram, what A and λ represent.
2. A radio wave transmitted from a certain radio station is represented by the wave equation given below, where x and y are in metres while t is in seconds. Calculate the (i) wavelength of the wave, (ii) frequency of the wave, (iii) velocity of the wave.