TOPIC 1: WAVES – PHYSICS NOTES FORM 4

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WHAT IS A WAVE?

A wave is a period disturbance which transfers energy from one place to another.

There are two types of waves:

• Mechanical waves
• Electromagnetic waves

1. MECHANICAL WAVES

The mechanical waves are the waves which propagated through material medium such as solid, liquid or gas a speed which depends on the elastic and inertia properties of the material medium.

There are two types of mechanical wave;
(a)Longitudinal waves

(b)Transverse waves

(a). LONGITUDINAL WAVES

A longitudinal wave is a mechanical wave whose particle displacement is parallel to the direction of the wave’s propagation .The particles in the medium are forced to oscillate along the same direction as that in which the waves is traveling.

Example;

If a horizontal loose stinky spring is set into vibration horizontally the waves travels horizontally.

NOTE: The regions along the material medium with the high pressure are called compression and the region with pressure is called Rarefactions.

 

(b). TRANSVERSE WAVES

• A transverse wave is a wave in which the direction of the wave’s propagation is perpendicular to the direction of the particles displacement.

Example;

A loose horizontal slinky spring vibrates perpendicular to the waves which travels horizontally.

2. ELECTROMAGNETIC WAVES

Electromagnetic wave is a wave which does not necessary requires a material medium for its propagation and own also travel through vacuum. Examples of electromagnetic waves are radio waves, light waves, TV waves, x- ray, gamma rays, mobile phone waves etc.

The electromagnetic waves involves electric and magnetic field of the empty space vacuum acting perpendicular to each other

NB: The speed of all electromagnetic waves is 3.0×10⁸m/s

DIFFERENT BETWEEN MECHANICAL WAVES AND ELECTROMAGNETIC WAVES

MECHANICAL WAVES	ELECTROMAGNETIC WAVES
Can not be transmitted through a vacuum.	Can be transmitted even through vacuum.
They require material medium (solid liquid or gas) for propagation.	They do not require material medium for propagation.
Are causes by the vibrations of the particles of the material media through which they can pass.	Are caused by the effect of electric and magnetic field in the space.
Mechanical waves have low speed.	Electromagnetic waves have high speed.
Have long waves lengths.	Have short waves length.
Can be longitudinal or transverse waves.	Only transverse in nature.

WAVE PARAMETERS

A wave can be described fully by the following terms;

-Wave length

-Amplitude

-Time period

-Velocity

• Consider transverse waves ABCDE and EFGHI formed by a rope which one and is fixed to a pole and the other and is being moved up and down continuously.

 

 

1. Wavelength

• The distance between two nearest points on a waves which are in the same phase of vibration is called wavelength denoted by a Greek latter Lambda (λ) measured in meters (m).
• Points B and F are crests, the distance between them is the wavelength.
• Points D and H are trough the distance between them is the wavelength.

    NOTE

• A wavelength is the distance between two consecutive crests trough of a wave.
• A wavelength is the horizontal distance completed by one cycle of waves.

2. Amplitude

• An amplitude of a waves is a maximum displacement of particles of the material medium from their original undisturbed position.
• The amplitude of the wave denoted by the letter A measured in maters (m).
• This quantity (amplitude) tells us about the size of the waves (big or small).
• The amplitude of a waves can be also defined as the height of the crest or depth of the trough (refer the diagram)

• The BP, FR are the amplitude of the waves the (the height of the crest).

• The QD, SH are the amplitudes of the waves (the depth of the through).

3. Time period

• Time period is the time neared to produce one complete waves or vibration or oscillation or cycle or to and fro motion.
• The time period of a waves is denoted by T measured in second (s)

4. Frequency

• The frequency of waves is the number of complete waves or vibration or oscillation or cycle produce in one second.
• It is denoted by f measured in hertz (Hz)
• If 5 complete cycles / waves / vibrations are produces in one second then the frequency is 5Hz, if 100 complete vibrations are produces in one second then the frequency is 100Hz.

NB: 100Hz mean there are 1000 complete waves being produced in one second.

Example:

• Tuning forks are often marked with numbers like 512 Hz, 384 Hz, 256Hz, etc.   These numbers signify the frequency of vibration oscillation or cycles or waves of the tuning forks. Tuning forks of 512 Hz will make 512 vibrations per second and emit 512 Hz complete sound waves per second. When it is hit on hard surface.

5. VELOCITY

• The velocity or speed of waves is the distance traveled or moved by waves in one second.
• The velocity or speed of a waves is denoted by V measured in meter per second (m/s)

THE RELATIONSHIP BETWEEN VELOCITY, TIME PERIOD, FREQUENCY, AND WAVES LENGTH

• If the distance traveled by a waves is numerically equal to its wavelength (λ), Then the time taken by the wave is equivalents to time period (T)

From;   V = λ x f

Hence;     V =     λ x f

   V =     λf  

Where   V   =   velocity

λ =   wavelength

f   =   frequency

This equation is known as WAVE EQUATION

Example;

1. Calculate the velocity of the wave whose wavelength is 1. 7 x10^-2m and frequency 2×10¹⁴Hz

Solution

Data given

λ   =   1.7 X 10^-2m

f     =     2×10¹⁴Hz

From; 

V   = λf

= 1.7 x 10^-2 x2 10 ¹⁴

= 3.4 x 10¹²m/s

The velocity of the wave is 3.4 1×10¹²m/s

1. Find the wavelength of sound wave whose frequency is 550Hz and speed is 330m/s

Solution

Data given

f   =   550Hz

V   =   330m/s

From 

V     =     λf

The wavelength is   0. 6m

NB: The higher the frequency of a wave, the shorter the wavelength and the lower is the frequency on the wave, the longer is the wavelength.

3. The radio waves have a velocity of about 3.0 x10⁸m/s and the wavelength of 1500m. Calculate the frequency of these waves?

Solution

Data given

V     =   3.0 x 10⁸m/s

λ=   1500m

f       =   ?

From: V   =   λf

f =     2.0 x 10⁵ Hz

4. The frequency is 2. 0 x 10⁵ Hz

 

The figure illustrates part of a wave traveling across the water at a particular place with velocity of 2m/s.  Calculate;

1. The amplitude of the wave.
2. The frequency of the wave.
3. The wavelength of the wave.

(a) The amplitude of the wave is 0.2cm

The wavelength is 0. 2m

5. The wavelength of signals from a radio transmitter is 1500m and the frequency is the 200KHz. What speed to the radio wave travel?

•What is the wavelength of a transmitter operating at 1000KHz?

Solution

λ=     1500m

f   = 200 KHz= 2, 00,000Hz

From;

V   =λf

= 1500 x 200, 000

= 300, 000, 000 m/s

The velocity of the wave length is 3.0 x 10⁸m/s

f= 1000KHz  = 1,000,000 Hz = 1.0 x 10⁶ Hz

V  = 3.0 x10⁸m/s

λ=?

V = λf

= 3. 0 x 10²m

The wavelength is 3. 0 x 10²m

6. A certain wave has time period of 0.04 second and travels at, 30 X 10⁷ m/s Find its wavelength.

Solution

Data:

T = 0.04 sec

V = 30 x10⁷m/s

=λ     ?

From;

λ =   VT

= 30 x 10⁷ x 0.04

= 3.0 x10⁸ x 4.0 x10^-2

= 1.2 x10⁷m

It is wavelength   is 1.2 x10⁷m

 7.  A personal with deep voice singing a note of frequency 200Hz is producing sound waves whose velocity is 330m/s.find the sound’s wave length.

Solution

Data

f = 200Hz

V = 330m/s

From;

V=λ f

λ   = 1.65m

8. The frequency of oxygen is 20 x 10¹³Hz. find it’s wavelengths.

          Solution

Data

f = 20 x10¹³Hz

V = 3.0 x 10⁸m/s

From:  V= λf

= 1.5 x 10^-6m

The wavelength is   1.5 x 10^-6m

TOPIC 1: WAVES – PHYSICS NOTES FORM 4

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