5
1 Physics 202, Lecture 20 Today’s Topics Wave Motion General Wave Transverse And Longitudinal Waves Wave speed on string Reflection and Transmission of Waves Wave Function Sinusoidal Waves Standing Waves 1 General Waves Wave: Propagation of a physical quantity in space over time q = q(x, t) Examples of waves: Water wave, wave on string, sound wave, electromagnetic wave, “light”, quantum wave…. Mechanical wave: Propagation of small motion (“disturbance”) in a medium. Physical quantity to be propagated: displacement. Recall: Displacement is a vector. 2 Transverse and Longitudinal Waves If the direction of mechanic disturbance (displacement) is perpendicular to the direction of wave motion, the wave is called transverse wave. If the direction of mechanic disturbance (displacement) is parallel to the direction of wave motion, the wave is called longitudinal wave. see demos. In general, a wave can be a combination of the above modes. The definition can be extended to other (non- mechanical) waves. e.g Electromagnetic waves are always transverse. 3 Electromagnetic Waves are Transverse x y z E B c Two polarizations possible 4

Transverse and Longitudinal Waves Electromagnetic Waves are Transverse · 1 Physics 202, Lecture 20 Today’s Topics Wave Motion General Wave Transverse And Longitudinal Waves Wave

Embed Size (px)

Citation preview

Page 1: Transverse and Longitudinal Waves Electromagnetic Waves are Transverse · 1 Physics 202, Lecture 20 Today’s Topics Wave Motion General Wave Transverse And Longitudinal Waves Wave

1

Physics 202, Lecture 20

Today’s Topics   Wave Motion

  General Wave   Transverse And Longitudinal Waves   Wave speed on string   Reflection and Transmission of Waves

  Wave Function   Sinusoidal Waves   Standing Waves

1

General Waves   Wave: Propagation of a physical quantity in space over time q = q(x, t)

  Examples of waves: Water wave, wave on string, sound wave, electromagnetic wave, “light”, quantum wave….  Mechanical wave: Propagation of small motion (“disturbance”) in a medium.

 Physical quantity to be propagated: displacement.

Recall: Displacement is a vector. 2

Transverse and Longitudinal Waves   If the direction of mechanic disturbance

(displacement) is perpendicular to the direction of wave motion, the wave is called transverse wave.

  If the direction of mechanic disturbance (displacement) is parallel to the direction of wave motion, the wave is called longitudinal wave.

 see demos.

  In general, a wave can be a combination of the above modes.

  The definition can be extended to other (non-mechanical) waves.   e.g Electromagnetic waves are always transverse.

3

Electromagnetic Waves are Transverse

x

y

z

E

B c

Two polarizations possible 4

Page 2: Transverse and Longitudinal Waves Electromagnetic Waves are Transverse · 1 Physics 202, Lecture 20 Today’s Topics Wave Motion General Wave Transverse And Longitudinal Waves Wave

2

Seismic Waves (motion in earthquakes)

Longitudinal

Transverse

Transverse

Transverse

5

Wave On A Stretched Rope   It is a transverse wave See demos.

  The wave speed is determined by the tension and the linear density of the rope:

lmTvΔΔ

≡= µµ

;

6

Reflection of wave on string from hard and soft walls

7

Hard wall reflected wave is inverted

Soft wall reflected wave is not inverted

Reflection and Transmission of Waves

8

Page 3: Transverse and Longitudinal Waves Electromagnetic Waves are Transverse · 1 Physics 202, Lecture 20 Today’s Topics Wave Motion General Wave Transverse And Longitudinal Waves Wave

3

Wave Function   Waves are described by wave functions in the form:

y(x,t) = f(x-vt)

y: A certain physical quantity e.g. displacement in y direction

f: Can have any form

x: space position. Coefficient arranged to be 1

t: time. Its coefficient v is the wave speed v>0 moving right v<0 moving left

9

An Exercise to Explain Wave Speed   A wave is described by function y=f(x-vt).

  At time t1 in position x1, how large is the quantity y?   y= f(x1-vt1) = y1

  At a later time t2=t1+Δt, what is y at position x2=x1+vΔt?

  y2= f(x2-vt2) = f(x1+vΔt -v(t1+Δt))= f(x1-vt1) = y1

  How to interpret the result?   Between t1 and t1+Δt, the value y1 has

transmitted from position x1 to x1+vΔt  speed = (x1+vΔt - x1 )/(t1+Δt - t1 ) =v i.e v>0 moving right; v<0 moving left;

10

Linear Wave Equation  Linear wave equation

2

2

22

2 1ty

vxy

∂∂

=∂∂

certain physical quantity

Wave speed

 Sinusoidal wave

)22sin( φπλπ

+−= ftxAy

A:Amplitude

f: frequency φ:Phase

General wave: superposition of sinusoidal waves

v=λf k=2π/λ ω=2πf

λ:wavelength

11

Parameters For A Sinusoidal Wave   Snapshot with fixed t: wave length λ=2π/k   Snapshot with fixed x: angular frequency = ω frequency f =ω/2π Period T=1/f Amplitude =A   Wave Speed v=ω/k v=λf, or v=λ/T   Phase angle difference

between two positions Δφ =-kΔx

Snapshot:Fixed t

Snapshot:Fixed x 12

Page 4: Transverse and Longitudinal Waves Electromagnetic Waves are Transverse · 1 Physics 202, Lecture 20 Today’s Topics Wave Motion General Wave Transverse And Longitudinal Waves Wave

4

Standing Waves  When two waves of the same amplitude, same

frequency but opposite direction meet standing waves occur.

y1 = Asin(kx −ωt)

y2 = Asin(kx +ωt)

y = y1 + y2 = 2Asin(kx)cos(ωt) Points of destructive interference (nodes)

kx = nπ; x =nπk

=nλ2

; n =1,2,3...

 Points of constructive interference (antinodes)

kx = (2n −1) π2

; x = (2n −1) λ4

; n =1,2,3...13

Standing Waves (cont)

 Nodes and antinodes will occur at the same positions, giving impression that wave is standing

14

Standing Waves (cont)  Standing waves with a string of given length L are

produced by waves of natural frequencies or resonant frequencies:

λ =2Ln

; n =1,2,3...

f =vλ

=nv2L

=Tµ

n2L

15

Sound travels at 340 m/s in air and 1500 m/s in water. A sound of 256 Hz is made under water. In the air,

A.  the frequency remains the same but the wavelength is shorter.

B.  the frequency remains the same but the wavelength is longer.

C.  the frequency is lower and the wavelength remains the same.

D.  the frequency is higher and the wavelength remains the same.

E.  both the frequency and the wavelength remain the same.

Page 5: Transverse and Longitudinal Waves Electromagnetic Waves are Transverse · 1 Physics 202, Lecture 20 Today’s Topics Wave Motion General Wave Transverse And Longitudinal Waves Wave

5

Sound travels at 340 m/s in air and 1500 m/s in water. A sound of 256 Hz is made under water. In the air,

A.  the frequency remains the same but the wavelength is shorter.

B.  the frequency remains the same but the wavelength is longer.

C.  the frequency is lower and the wavelength remains the same.

D.  the frequency is higher and the wavelength remains the same.

E.  both the frequency and the wavelength remain the same.

We can hear sounds that are produced around a corner but cannot see light that is produced around a corner because

A.  light travels only in straight lines whereas sound can travel in a curved path.

B.  sound has more energy than light.

C.  sound has shorter wavelengths than light.

D.  sound has longer wavelengths than light.

E.  None of these is correct.

We can hear sounds that are produced around a corner but cannot see light that is produced around a corner because

A.  light travels only in straight lines whereas sound can travel in a curved path.

B.  sound has more energy than light.

C.  sound has shorter wavelengths than light.

D.  sound has longer wavelengths than light.

E.  None of these is correct.