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CHAPTER 7: WAVES

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INTRODUCTION

What is a wave?

  • Wave is a method of propagation of energy.
  • A wave is an oscillation that travels from one place to another.
  • A wave also is a disturbance that travels through a medium from one location to another location.
  • Wave also carries energy from one place to another.
  • For example, when we drop a ball into a pond of still water, a few circular ripples move outwards, on the surface of the water. As these circular ripples spread out, energy is being carried with them.

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Wave motion is the transfer of energy from one place to another

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The particles of the medium (rope, spring, water) only vibrate about their equilibrium position, but the energy travels forward.

WAVE MOTION?

https://youtu.be/sRbSQ9wGA1I?si=fBCjdZ6xl6DNrA3R -slinky spring

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

https://youtu.be/4NHyuHhh59g?si=h3-gBpTjgW4Mf2d2 -ripple tank

CONCLUSION FROM SIMULATIONS:

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  • Waves transfer energy, not matter.
  • Particles oscillate about equilibrium position.

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Do you know ‘Mexican Wave’?

Similar idea..

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Describing waves

IMPORTANT TERMS

displacement-distance graph

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Period = 1

Frequency

displacement-time graph

time

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Ans: D

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6) Phase difference - the difference in the stage of oscillation between two points in a wave (or between two waves) at a given time.

https://youtu.be/v_oujF9RHK8?si=-y2AshloKxAOSZ8e – phase difference explanation

USEFULL RELATIONSHIP:

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Phase difference/ 360 degree

=

Path difference /wavelength

=

time/period

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because 1 oscillation /1 cycle = 1 T (period) = 360 degree = 1 lambda (wavelength)

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Try This!

Ans: C

Ans: D

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Ans: C

(all answer in degree)

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Ans: B

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HINT:

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Using Cathode Ray Oscilloscope (CRO)

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Dual trace – we have 2 waves

Signal generator – produce waves

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Ans: A

Ans: A

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DERIVITION OF WAVE EQUATION

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Ans: C

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  • The source of any wave is a vibration or oscillation.
  • For example, the forming of the slinky waves as shown.
  • Wave motion provides a mechanism for the transfer of energy from one point to another

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Sources of Waves

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  • Classified by what they move through:

1. Mechanical Waves

    • Mechanical waves require a medium, propagate by the vibration of material particles such as air, to travel through. An example of a mechanical wave is a sound wave, which requires air to travel.

2. Electromagnetic waves (EM Waves)

    • Do not require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields generated by charged particles, and can therefore travel through a vacuum.
    • e.g.,radio waves, microwaves,  X-rays and gamma rays.

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Electromagnetic Spectrum

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  • There are two types of mechanical waves:
    • Stationary (standing) waves
    • Progressive (travelling) waves

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  • Waves that move through a material or medium are called progressive waves.

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  • A progressive waves transfers energy from one position to another.

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  • One of the characteristics of a progressive wave is that it carries energy.
  • As a disturbance moves through a medium from one particle to its adjacent particle, energy is being transported from one end of the medium to the other.
  • Thus, the energy transported by a wave is proportional to the square of the amplitude.

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  • where k = 4π2mf2

PROGRESSIVE WAVES- AMOUNT OF ENERGY

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The intensity of a wave, I is defined as the power transported across unit area perpendicular to the direction of energy flow:

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SI unit of intensity is Watts per square meter (W/m2).

Intensity of Waves

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  • The intensity is proportional to the square of the amplitude of a wave.

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  • Thus, doubling the amplitude of a wave increase the intensity of the wave by a factor of four.

Intensity of Waves

 

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  • If a wave is able to spread out three-dimensionally from its source, and the medium is uniform, the wave is a spherical wave.

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  • As the waves moves outward, the energy it carries is spread over a larger and larger area since the surface area of a sphere of radius r is .

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  • Thus, the intensity of a spherical wave is :

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If we consider two points at distances r1 and r2 from the source, then :

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where :

I1 = intensity at point 1

I2 = intensity at point 2

A1 = amplitude at point 1

A2 = amplitude at point 2

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ANS : C

https://www.flippingphysics.com/sound.html

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ANS : D

https://www.flippingphysics.com/sound.html

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https://phet.colorado.edu/sims/html/waves-intro/latest/waves-intro_en.html

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  • Progressive waves move through a material.

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  • They distribute energy from a point source to a surrounding area. They move energy in the form of vibrating particles or fields.

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  • There are two different types of progressive waves:
    • Transverse waves
    • Longitudinal waves

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Longitudinal Waves vs Transverse Waves

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https://www.acs.psu.edu/drussell/demos/waves/Lwave-Red-2.gif

The animation shows the difference between the oscillatory motion of individual particles and the propagation of the wave through the medium. The animation also identifies the regions of compression and rarefaction.

Longitudinal Waves

https://www.flippingphysics.com/sound.html

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  • Longitudinal waves - vibrations (of particles) are parallel to the wave motion (direction).
  • So if the wave is travelling horizontally, the particles will be compressed closer together horizontally, or expanded horizontally as they go along. The particle movement is a series of compressions. For example, sound waves, p-wave from Earthquake

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Longitudinal Waves

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  • Transverse waves - vibrations are perpendicular to the wave motion
  • So, if the wave is travelling horizontally, the vibrations will be up and down. For example, water waves, string vibration.

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Transverse Waves

https://www.geogebra.org/m/uamtnuuk

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Fill in the blank time..

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ANS: C

ANS: A

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Ans: C

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THE DOPPLER EFFECT

  • The Doppler effect, is the shift in frequency of a sound due to motion of the source or the observer.

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  • Definition of Doppler effect is change in frequency is caused by a relative motion between source and observer.

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  • These occurs for all types of waves.
  • An example of application- doppler radar

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https://youtu.be/VjhAh5v14R4?si=8wRp79LTyqGOJZa0 – radar for weather forecast

https://youtu.be/xpIRqdxqDyY?si=87JXbGQa5hdILj6Z - radar for aeroplane

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�

Case 1�source moving towards observer��

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�Case 1�source moving towards (approaching) observer��

Case 2�source moving away

(receding) observer��You may try to derive the equation for Case 2 by yourself

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  • Derivation of Doppler effect equation

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https://youtu.be/_mpIwJ6hkPw

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  • With the + sign = a receding source
  • With the – sign = an approaching source

 

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EM waves is the wave transmitted by vibration of electric and magnetic fields at right angles to the direction of propagation.

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Electromagnetic Wave

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v = fʎ

E = hf

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v = fʎ

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ANS: C

ANS: D

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Polarisers - optical filters that only allow oscillations in one plane, thus blocking some of the light

https://youtube.com/shorts/haoE2P9DlFA?si=zPHYhJbZStMPOdbK

polarizing filter

Polarization by Transmission

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Polarized and Unpolarized EM Waves- Transverse Wave

Light from the Sun, an incandescent lamp, or a candle flame is unpolarized light.

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When this light passes through a polarizing filter, only one direction of vibration is allowed to pass through — the result is plane polarized light.

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What kind of waves can be polarized?

All transverse waves such as

Wave in string

Light

Plane polarized:

wave is always in a single fixed plane

SURE, CAN

CANNOT!

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Light waves are transverse waves, so can be polarized

RECALL: Light consists of perpendicular oscillating electric and magnetic fields

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We can concentrate on the electric field , E in this discussion since

it is the one our eyes perceive

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Example of application- How polarization reduced glare by using a sunglasses by reflection

When unpolarized light strikes a nonmetallic horizontal surface (like water or glass):

The reflected light becomes partially polarized, with horizontal polarization dominant.

Your eyes receive mostly horizontally polarized light from reflections → intense glare, reducing contrast and visibility.

Polarized sunglasses have a polarizing filter built into their lenses.

  • The transmission axis of this filter is vertical.
  • It BLOCKS horizontal electric field components — the ones responsible for glare.
  • So, only vertically polarized light (from natural surroundings) passes through.

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What happens when polarized light is passed through additional filters?

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According to Malus’s Law:

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I = I0cos2 θ

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where

I = transmited intensity

I0 = incident intensity

θ = angle between E-field and filter’s transmission axis

Intensity proportional with Amplitude squared

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Polarizers and Analyzers

Polarizer: a polarizing filter used to produce polarized light

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Analyzer: a polarizing filter used to determine if light is polarized

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Unpolarized light’s intensity is reduced by 50% when passing through a polarizer regardless of the orientation

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Already polarized light’s intensity is reduced depending on orientation of polarizer/analyzer according to Malus’s Law

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Intensity proportional with Amplitude squared

I α A2

E is electric field amplitude, not energy

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https://www.geogebra.org/m/E6jZ52vK - 3 slits polarization��https://www.geogebra.org/m/dgedzmz3#material/x5w3XjJs -Malu’s law��https://www.geogebra.org/m/dgedzmz3#material/nxqRUBJm -3D polarizer

When unpolarized light pass a polarizer, Intensity, I reduced by half.

I after = I initial /2

I = Io/2

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When plane polarized light pass a polarizer, we can find the Intensity by using Malu’s Law

I after = I initial cos theta squared

I = Io cos θ2

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Ans: B

Ans: A

Ans: C

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QUESTION 1

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QUESTION 2