1© Manhattan Press (H.K.) Ltd. Pulse Continuous waves Continuous waves 8.1 Characteristics of waves...

© Manhattan Press (H.K.) Ltd. 1

• PulsePulse

• • Continuous wavesContinuous waves

8.1 Characteristics 8.1 Characteristics

of wavesof waves

• • Wave motionWave motion

• • Graphical representation of wavesGraphical representation of waves

• • Factors affecting the speed of wavesFactors affecting the speed of waves

• • Wave intensityWave intensity


8.1 Characteristics of waves (SB p. 2)

A wave is generated when there are disturbances repeated periodically.

How to generate a wave?


Classify a wave according to …

Energy transfer:

i.e. progressive waves VS stationary waves

Medium of propagation:

i.e. mechanical waves VS electromagnetic waves

Direction of oscillation of particles:

i.e. transverse waves VS longitudinal waves



Pulse

A pulse on a slinky spring is produced by

moving the end of it …


forth and back

up and down


Characteristics of a pulse

1. The pulse carries energy from one end

to the other end of the spring.

2. The pulse moves with constant speed

along the spring.

3. Each particle in the spring is displaced through

a small distance before returning

to its original position.


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More to Know 1More to Know 1


Continuous waves

If a rope is shaken continuously up and down,

a series of pulses called a wave is produced.


Equilibrium positions

wavelengthcrest

trough amplitude

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Wave motion - a complete oscillation


t = 0

Tt41

Tt21

Tt43

t = T


Velocity, frequency & wavelength


taken Time

ntDisplaceme waveofVelocity

Tλv

fv


Frequency & period


The The frequency ( frequency ( ff ) ) of a wave is the number of of a wave is the number of completed oscillations per second. oscillations per second.

Tf 1

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Example 1Example 1


Wave intensity


The intensity (I) of a wave is the rate at which energy is transferred by the wave to a unit area which is perpendicular to the direction of propagation of the wave.

API

where where PP is the source power and is the source power and AA is the surface area. is the surface area. The unit is W mThe unit is W m–2–2..


Wave intensity


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Example 2Example 2

I a2

For a sinusoidal wave moving through a For a sinusoidal wave moving through a medium, each particle in the medium moves in medium, each particle in the medium moves in simple harmonic motionsimple harmonic motion. .

Since the energy of a particle moving in simple Since the energy of a particle moving in simple harmonic motion with amplitude harmonic motion with amplitude aa is , is , we have:we have:


Graphical representation of waves


The displacement-time graph shows the The displacement-time graph shows the displacement of a particle at different times.displacement of a particle at different times.

1. Displacement-time graph1. Displacement-time graph

If the motion of the source is If the motion of the source is simple harmonic, the simple harmonic, the displacement-time graph is adisplacement-time graph is a sinesine function. function.


Graphical representation of waves


The displacement-distance graph shows the The displacement-distance graph shows the displacement of particles at different positions displacement of particles at different positions at one instant.at one instant.

2. Displacement-distance graph2. Displacement-distance graph


Instantaneous motion of particles


Particles Particles dd, , ee, , ff are are moving upmoving up

Particles Particles aa, , bb, , hh,, i i, , jj are moving downare moving down

Particles Particles cc, , gg, , kk are are momentarily at restmomentarily at rest

Particles Particles aa, , ee, , ii are of are of highest highest speed speed

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Example 3Example 3


1. All electromagnetic waves have same speed 1. All electromagnetic waves have same speed in vacuum but different speeds in a medium:in vacuum but different speeds in a medium:

Wave speed in a medium:Wave speed in a medium:


Factors affecting the speed of waves

where where cc = speed of light, = speed of light,

nnrr = refractive index of the medium. = refractive index of the medium.Go to




Factors affecting the speed of waves

2. The propagation of mechanical waves 2. The propagation of mechanical waves depends on the depends on the vibrationsvibrations of particles in the of particles in the medium. medium.

Therefore, the wave speed depends on the Therefore, the wave speed depends on the massmass and and elasticityelasticity of the medium. of the medium.

If the mass of the particles in the medium is If the mass of the particles in the medium is greatergreater, the wave speed is , the wave speed is lowerlower..

If the elasticity of medium is If the elasticity of medium is greatergreater, the wave , the wave speed isspeed is higher higher..


Wave speed


(b) The speed of longitudinal wave in solid is:

where E = Young modulus, = density

E v

(a) The speed of transverse wave along a stretched

string is:

where T = tension, = mass per unit length

μT v

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Example 4Example 4


End


Energy transfer

A wave can transport energy from one place to another without the transfer of matter.

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Periodic motion

Wave motion is a periodic motion.

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Q: Q: A typical sound wave of human speech has a frequency of 600 Hz, whereas the frequency of red light is about 4.3 × 1014 Hz.In air, light travels at 3 × 108 m s–1 and sound at 344 m s–1. Find the wavelengths of the two waves.

Solution



Solution:Solution:

For both waves, v = fλ

For the sound wave:

λ =

=

= 0.57 m

For the light wave:

λ =

= 6.98 × 10–7 m

fv

600344

14

8

10 3.410 3 Return to

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Q: Q: A light source has an average power of 200 W. Calculate the intensity of the light source at a point 6 m from the source.

Solution



Solution:Solution:

The wave intensity is given by

I =

=

= 0.44 W m–2

24 rP

2)6(4200

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Q: Q: The figure shows the simple harmonic motion

of a particle in a medium through which a

wave is moving with a speed of 5.0 km s–1 from left to right.

What is (a) the frequency of oscillation, (b) the amplitude of oscillation, and (c) the wavelength of the wave? Solution



Solution:Solution:

(a) From the graph, period of oscillation, T = 20 s

Frequency, f =

=

= 5.0 104 Hz

(b) Amplitude of oscillation = 2 m

(c) Using v = f ,

Wavelength, =

= = 0.1 m

T1

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TextTextfv

4

3

10 0.510 0.5

610 201


Young modulus

Young modulus is a measure of the stiffness of a material.

It is defined as: E =

where σ = tensile stress; ε = tensile strain.

Young modulus and the concept of elasticity will be discussed in more detail under the topic of Matter.


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Q: Q: The tension on the longest string of a piano

is 1 088 N, and the mass per unit length of this

string is 0.064 kg m–1. What is the speed of a

wave on this string?Solution



Solution:Solution:

The wave speed on this string is:

v =

=

= 130.38 m s–1

T

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064.01088

1© Manhattan Press (H.K.) Ltd. Pulse Continuous waves Continuous waves 8.1 Characteristics of waves...

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