1.      Waves

1.1.            Progressive waves

a.       describe what is meant by wave motion as illustrated by vibration in ropes, springs and ripple tanks.

b.      understand and use the terms displacement, amplitude, phase difference, period, frequency, wavelength, and speed.

c.       deduce, from the definitions of speed, frequency and wavelength, the wave equation v = f λ 

d.      recall and use the equation v = f λ

e.      understand that energy is transferred by a progressive wave.

f.        recall and use the relationship intensity ∝ (amplitude)²

 

1.1  PROGRESSIVE WAVE

Wave motion is a means of moving energy from place to pace. Waves which transfer energy from place to place without the transfer of matter are called progressive waves.

Examples

a.      ropes, springs and ripple tanks

b.      Waves from the sun carry energy  that plants need to survive and grow.

c.       Energy carried by sound waves cause our eardrums to vibrate

Progressive waves are classified as transverse or longitudinal waves.

In transverse waves movement of particles are at right angles to the movement of energy. Examples of transverse waves include vibrations on a string and ripples on the surface of the water. We can make a horizontal transverse wave by moving the slinky vertically up and down. Light, Radio wave, water waves are a few examples of transverse waves.

In longitudinal waves, the movement of particles is usually parallel to the movement of energy. An example of longitudinal waves is compressions moving along a slinky. We can make a longitudinal wave by pushing and pulling the slinky horizontally. Longitudinal waves travel in the form of compression and rarefaction. The best example of longitudinal waves are sound waves.

 

 

A. Displacement

The displacement of a particle on a wave is its distance in a specified direction from its mean position.

B. Amplitude

The amplitude of the wave motion is defined as the maximum displacement of a particle in the wave.

C. Wavelength

It can be noted from figure above that the wave repeats. The wave can be reconstructed by repeating a section of the wave. The length of the smallest repeated unit is called its wavelength.

The wavelength is the shortest distance between two peaks, or the shortest distance between two troughs. It can also be defined as the distance moved by the wavefront during one oscillation of the source of the waves. The symbol for wavelength is λ (Greek letter lambda).

D. Period

Waves can also be represented by plotting the displacement in the y-axis and time in the x-axis, as shown in Figure below. The wave repeats after a certain interval of time. The time for one complete vibration is called the period (T) of the wave. The period of the wave is the time for a particle in the wave to complete one vibration, or one cycle.

E. Frequency

The number of complete vibrations (cycles) per unit time is called the frequency (f) of the wave. For waves on ropes or strings, displacement and amplitude are measured in mm, m or other units of length. Period is measured in seconds (s). The unit for frequency is per second (s-1) or Hertz (Hz).

F. Phase

Phase is used to describe the relative positions of the crests or troughs of two different waves of the same frequency. When the crests and troughs of the two waves are aligned, the waves are said to be in phase. When crests and troughs are not aligned, the waves are said to have a phase difference. When a crest and a trough of two waves are aligned, the waves are said to be in antiphase. Phase is measured in degrees or radians.

 Phase Difference Between Two Waves

Consider the two waves shown in Figure above. Both the waves are of the same frequency, but with a phase difference between them. The period (T) corresponds to a phase angle of 2π or 360°. The two waves are out of step by a time (t). Thus,

Phase difference of the waves of wavelength λ, which are out of step by a distance x,

From the definition of wavelength λ, in one cycle of the source, the wave energy moves a distance λ. The time taken for one cycle is the time period (T).

 

 

G. Path difference

Difference in distance travelled by two waves is called the path difference. The phase difference may be produced by allowing the two sets of waves to travel different distances – this difference in distance of travel is called the path difference.

The two waves illustrated in the following figure have phase difference (π/2) and path difference(λ/4).

Path Difference and Phase Difference

H. Intensity

Progressive waves carry energy. The amount of energy passing through unit area per unit time is called intensity. It is the power per unit area.

For a wave of frequency f and amplitude A, the intensity I is proportional to A² f²

The intensity   implying that  intensity decreases with increasing distance from the source.  I inversely proportional to r²

 Summary

●        Waves which move from place to place without the transfer of matter are called progressive waves.

●        The displacement of a particle on a wave is its distance in a specified direction from its position.

●        The amplitude of the wave motion is defined as the maximum displacement of a particle in the wave.

●        The wavelength is the shortest distance between two peaks or the shortest distance between two troughs. It can also be defined as the distance moved by the wave front during one oscillation of the source of the waves.

●        The period of the wave is the time for a particle in the wave to complete one vibration, or one cycle.

●        The number of complete vibrations (cycles) per unit time is called the frequency (f) of the wave.

●        When the crests and troughs of the two waves are aligned, the waves are said to be in phase. When crests and troughs are not aligned, the waves are said to have a phase difference. When a crest and a trough of two waves are aligned, the waves are said to be in antiphase.

●        Difference in distance travelled by two waves is called the path difference

 

USE OF TECHNOLOGY. PHET SIMULATIONS

https://phet.colorado.edu/en/simulations/waves-intro

https://phet.colorado.edu/sims/html/wave-on-a-string/latest/wave-on-a-string_en.html

 

WORKSHEET 1

1.      The period T of the waves shown below is 3.0 seconds and time between the waves  t is 0.25 seconds. Calculate the phase difference between the two waves in a) degrees b) radians.

2.      Two waves of the same frequency have a time period of 3.0 seconds. The two waves are out of phase by a time difference of 0.5 seconds. Calculate the phase difference between the two waves in degrees and radians.

3.      A turning fork of frequency 180 Hz produces sound waves of 2.0 m. Calculate the speed of the sound

4.      The amplitude of a wave in a rope is 15 mm. If the amplitude were changed to 25 mm, keeping the frequency the same, by what factor would the power carried by the rope charge?