PHYSICS As LEVEL(FORM FIVE) NOTES – WAVE MOTION-1(1)

• A wave is a periodic disturbance which propagate energy from a point in to another.
• Waves transfer energy from point to another point without carrying matter.

1. Mechanical waves
2. Electromagnetic waves

1. waves on a spring
2. water waves
3. sound waves
4. waves on stretched string (e.g. in musical instruments)

• mechanical waves require a material
  medium to transfer energy.
• when a mechanical waves travel through a medium the particle that make up the medium are disturb from their rest or equilibrium positions.

• Electromagnetic waves do not require a material medium to transfer energy.
• They can travel through a vacuum.

1. visible light
2. radio waves
3. infra-red radiation iv. ultraviolet radiation

5. gamma radiation
6. X-rays

1. Stationary / Standing waves
2. Progressive waves

1. STATIONARY / STANDING WAVE

2. PROGRESSIVE WAVE

1. Water waves
2. Wave on a string
3. Electromagnetic waves

• Sound waves

• A longitudinal wave is propagated by a series of compression and rarefaction

• Is a region of high pressure in a longitudinal wave.

• Is a region of low pressure in longitudinal wave.

• The crest and trough (valleys) in transverse wave can be likened to compression and rarefaction respectively in a longitudinal wave.
• Thus we may represent any wave by a single diagram as shown bellow:-

1. Amplitude
2. Wavelength iii. Frequency iv. Speed/ Velocity of propagation

• Symbol, A

• The SI unit of amplitude is the meter( m)

• Symbol, (Greek letter ―lambda‖),λ
• This is the distance between two successive points of equal phase in a wave.

• The wave length of a wave is the distance between two successive or adjacent crest or trough.
• It is a distance that the wave travels in the complete cycle.

• The S.I unit of wavelength is the meter,m
• Other unit in common use are:

-ƒ

• By definition

f

• Hence the S.I unit of frequency is the Hertz (HZ).

• This is the distance covered by the wave in unit time.

V

V

• Symbol, T

• It is the time taken for the wave to travel through a distance equal one wavelength -The S.I unit for period is the second (S)

• From the definition of V

• This is an angular displacement of a given wave particle in time t.
• This term is usefully in comparing two wave motions.
• Two waves are said to be in phase if their maximum and minimum values occur at the same instant otherwise there is said to be a phase difference

• Symbol, Ø
• This is the difference in phase between two wave motion
• If the phase difference is radians then the two waves are in ant phase (out of phase)

EXPRESSION OF PHASE DIFFERENCE

• Consider two particle O and P along the path of the waves

• Let O be origin of the wave
• A particle at P a distance X right of O will vibrate in different phase with the particle at O. – Let Ø be phase different between O and P
• Now

2 rad

PROGRESSIVE/ TRAVELING WAVE

THE PROGRESSIVE/ TRAVELING WAVE EQUATION

• Consider a progressive / traveling wave which is moving from left to right with a velocity V.

• Let O be origin of the wave

• If the wave generate travel from left to right then a particle at P, distance X from O will lag behind the particles at O by a phase angle Ø given by

Ø. …………………………..(i)

• For the displacement y of the particle at P we have:

where k = 2π/ λ ƒ = frequency

1. What is a wave?
2. Y = A sin is the equation

1. Frequency
2. Wavelength
3. Velocity

Y = A sin (t + kx)

1. Deduce whether the wave is traveling in the positive or negative x-direction.
2. If = 6.6 x 103 rad s-1 and k = 20m-1 calculate the speed of the wave in the medium

PATH DIFFERENCE

• This is difference in path length between two waves which meet at a point or between two points in a given wave.
• It is the distance corresponding to phase difference

CASE 1

CASE 2

• Consider two point P1 and P2 in the path of the wave from source

Path difference, ∆x

• from the expression of phase difference

• when x = ∆x = path difference, Ø

The equation y = A sin ( represent a plane wave traveling in a medium along the x direction y being the displacement at the point x at time t.

1. Deduce whether the wave is traveling in the positive x- direction or in the negative x- direction
2. ) If a = 1.0 x 10-7m, x 103s-1 and k = 20m-1 calculate

SUPERPOSITION OF WAVES

• The principle state “If two or more wave arrive at a point simultaneously then the resultant displacement at that point is the vector sum of the displacement due to individual waves”.

• Where y = resultant displacement

are the displacement due to individually waves.

Y1 = 5 sin ( ) and

Y2 = 5 sin ()

1. stationary waves

2. beats
3. interference

STATIONARY WAVES/STANDING WAVES

HOW A STATIONARY WAVE IS FORMED

• This is a point of minimum disturbance in a stationary wave system

• This is a point of maximum disturbance in a stationary wave system

THE EQUATION AT STATIONARY / STANDING WAVE

Y1 = A sin (

Y2 = A sin (

Y = A sin (

Y = A (sin (

Y= 2A sin (

Y = 2A sin

PROPERTIES OF A STATIONARY/STANDING WAVE

1. The distance between a node and its neighboring antinode is one quarter of a wavelength

2. All point along the wave have different amplitude.
3. Point between successive nodes are in phase.

DIFFERENCE BETWEEN PROGRESSIVE AND STATIONARY WAVES

1. Explain the difference between progressive waves and stationary wave
2. Progressive wave and stationary wave each has the same frequency of 250HZ and the same velocity of 30. Determine

(The phase difference between the vibrating points on the progressive wave which are 10cm apart

The distances between nodes in stationary wave

(Find the maximum displacement of motion at

( Find the positions of nodes and antinodes

( Does the function represent a travelling or stationary wave?

( Interpret the wave as superposition of two waves travelling in opposite directions

A standing wave on the string has nodes at What is the wavelength of the travelling wave?

Find: (Frequency and wavelength

(

Definition

AUDIBLE RANGE

ULTRASONIC SOUND

PROPAGATION OF SOUND WAVE

• It cannot be transmitted through a vacuum.

• If the particles are closer together, sound will travel faster.
• Hence sound travel with different velocities in different materials.

IN SOLID

Young’s modulus E of the solid.

Density of the solid.

IN FLUIDS

() Bulk modulus

() Density of the fluid

NEWTON’S FORMULA

• Newton assumed that the propagation of sound in a gas takes place under isothermal condition (constant temperature condition) in isothermal conditional Boyle`s law applies and hence: PV = K differentiating this equation:

• Where = change in pressure

• By definition:

1.013 x 105Pa

V = 280ms-1

• Laplace pointed out that Newton`s assumption of isothermal propagation is not correct.

REASON

Of air constant

P

………………………………(iii)

V =