Sec Notes - Waves

8/6/2019 Sec Notes - Waves

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WAVES

Waves transfer energy from one place to another. For example, sound waves transfer energyfrom the mouth of a person to the ears of another.

Light and sound travel by means of waves.

Although we do not see these waves of light and of sound, yet all of us are familiar with wavemotion. Dont we see waves at sea? But we do not mean waves when the sea is rough. Here wemean only small water waves.

Imagine that you are in the sea and a water wave comes along. As the wave passes you feelyourself being lifted up by the wave and then you feel yourself going down. And then you againfeel yourself lifted up and down again. And so on.This is because some of the water is being lifted up and some of the water is being pusheddown. This motion (or displacement) of the water can be represented by the graph below:

When the water is lifted up, its motion (or displacement) is plotted on the y-axis as positive onthe graph.When the water is pushed down, its motion (or displacement) is plotted on the y-axis as negativeon the graph.

The shape of the wave continues going up and down along to the RHS of the graph. That is awave consists of a repeated pattern. This means that a wave consists of repeated cycles.

The distance of one cycle is called the WAVELENGTH and the maximum displacement is calledthe AMPLITUDE as shown in the above diagram.

The number of cycles per second is called the FREQUENCY which is measured in Hertz (Hz).The time it takes to do one cycle is called the PERIOD which is measured in seconds (s).


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Two important formulae are:

frequency = 1/periodic time or period time = 1/frequency

f = 1/T or T = 1/f

wave speed = frequency x wavelength

v = f

The second formula is given in the SEC exam

Examples using these equations:

A loudspeaker reproduces a note of frequency 320Hz. It travels through the air with a speed of 340ms -1.a) What is the wavelength in air?

v = f v/f =

340ms -1 / 320Hz = 1.06m =

b) The sound passes through water where its wavelength is 4.5m.Calculate the speed of sound in water

v = f

v = 320Hz x 4.5mv = 1,440ms -1

c) The Sears Tower in Chicago sways back and forth in the wind with a frequency of about 0.12Hz. What is the period of vibration?

Period = 1/frequency

= 1 / 0.12

= 8.3s

Types of Wave: Transverse or Longitudinal?

There are two basic types of wave. These are:

a) Transverse

In a transverse wave the oscillation/vibration is perpendicular to the direction of travel.


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Sound travels through air because some of the air molecules get closer to each other (compression) andsome get far apart from each other.

Once again, LOOK AT THE WORD CAREFULLY!

The word rarefaction contains the word rare. That is there are fewer molecules. Molecules get rare.

This way you remember the meaning of the word rarefaction.

Problem. A longitudinal wave that has a frequency of 20.0 Hz travels along acoil spring. If the distance between successive compressions is 0.60 m,what is the speed of the wave?

The distance between successive compressions is the wavelength, .

Therefore v = f

v = 20.0 x 0.60

v = 12m/s.


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If you want to see a short video showing a longitudinal wave, go to the following website on theinternet:

http://www.youtube.com/watch?feature=player_detailpage&v=aguCWnbRETU

WAVES ARE REFLECTED, REFRACTED AND DIFFRACTED

We already know that light is reflected and refracted. All kind of waves can be reflected andrefracted. This can be seen with water waves in a ripple tank.

Problem:Five waves are generated every 0.1 s in a tank of water. What isthe speed of propagation of the wave if the wavelength of the surface

wave is 1.20 cm?

We are going to use v = f,

remember v is the velocity of the waves

f is the frequency, i.e. the number of waves per second
http://www.youtube.com/watch?feature=player_detailpage&v=aguCWnbRETUhttp://www.youtube.com/watch?feature=player_detailpage&v=aguCWnbRETU


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is the wavelength.

5 waves in 0.1s

? waves in 1s

then,5 x 1 / 0.1 = 50, hence the frequency = 50Hz

Therefore v = f,

v= 50 x 1.20

v = 60 cm/s

The arrow gives the direction of the

waves.The parallel lines are calledWAVEFRONTS.The distance between two successive

parallel lines is the wavelength.

REFRACTION of light means that light changes direction when itgoes from glass to air. That is light is changing the medium.

Even water waves show refraction. Water waves get refractedwhen the waves go from deep to shallow water.

Waves show also DIFFRACTION.Diffraction of waves means the spreading of waves when waves go through a very smallopening.


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On the RHS the opening is small and so thewaves spread almost in a semicircle.But on the LHS, the waves continue almostas parallel lines as before. They spreadonly a little. This is because the opening isnot small.

This photo shows diffraction of waves at the sea.Note the small opening through which the waves arepassing.

this is a diagram of the above photo.


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Now,Questions from the SEC exam


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Sec Notes - Waves