Physics 2 Exam 1

Waves

disturbance that transfers energy without transferring matter

parts of a wave

• crest

• trough

• amplitude

• wavelength

• frequency

• period (T)

crest

highest point

trough

lowest point

Amplitude(A)

Maximum displacement from equilibrium

Wavelength

Distance between identical points on consecutive waves

frequency (f)

Number of waves passing each second (Hz)

period (T)

• Time for one complete wave

  • T=1/f

wave speed formula

v = fλ

• v= wave speed

• f-= frequency

• λ = wavelength

Increasing frequency while speed stays constant decreases

wavelength

Superposition Principle

when two waves meet, their displacements add together

• 2 types (constructive and destructive)

Constructive interference

Two crests meet (or two troughs).

Result:

• Bigger amplitude

Occurs when waves are in phase.

Destructive Interference

A crest meets a trough. (opposites_

Result:

• Smaller amplitude

• Can completely cancel

Occurs when waves are out of phase

Standing Waves

• forms when two identical waves travel in opposite directions.

• Instead of traveling, the wave appears stationary.

Standing waves occur because o

resonance

Node

a point that never moves

characteristics of nodes

• Zero displacement

• Always stays still

• Created by destructive interference

antinodes

where vibration is greatest.

antinodes characteristics

• Maximum displacement

• Created by constructive interference

Harmonic

one possible standing-wave pattern.

first harmonic

• Fundamental frequency

• Lowest frequency possible

second harmonic

twice the fundamental frequency

third harmonic

three times the fundamental

the higher the harmonic the

higher the frequency, but shorter wavelength

A string fixed at both ends always has

nodes at the ends

• f =nv/2L​, where

  • n=harmonic number

  • L=length

• Also

• λ=2L/n

wave speed on a string formula

v = √T/μ

• T= tension

• μ = mass per unit length

• increasing tension → wave travels faster

• increasing mass density → wave travels slower

mass density formula

μ = m/L

• kg/m

Resonance

occurs when an object is driven at one of its natural frequencies.

result of resonance

large amplitude vibration

examples of resonance

• guitar strings

• piano strings

• organ pipes

Standing Waves in Tube

Air inside tubes vibrates just like strings.

Open-Open Tube

• Both ends are open.

• Ends are antinodes.

• Formula: λ=2L/n

• All harmonics exist.

Closed-Closed Tube

• Same equations as open-open.

• Both ends are nodes.

• All harmonics exist.

Open-Closed Tube

• One end closed.

• One end open.

• Closed end = node

• Open end = antinode

• Formula: λ=4L/ 2n-1

• only odd number harmonics exist (1,3,5,7)

beats

When two similar frequencies interfere.

• The closer the frequencies, the slower the beats

Light behaves as a

wave

Because of this, light shows

• interference

• diffraction

Double Slit Experiment

• Light passes through two narrow slits.

• Each slit acts like a new source.

• The two waves interfere.

Bright Fringes

constructive interference

• formula: dsinθ=mλ

Dark Fringes

Destructive interference.

• formula: dsinθ=(m+1/2​)λ

Fringe Position formula

y=mλL/d​

where

• L = distance to screen

• d = slit separation

Fringe Spacing formula

Δy=λL/d​

increasing wavelength →

fringes farther apart

increasing screen distance →

fringes farther apart

increasing split separation →

fringes closer together

Diffraction Grating

• has thousands of tiny slits.

• Formula: dsin⁡θ=mλ

• Different wavelengths leave at different angles.

• Used in spectroscopy.

Thin Film Interference

Occurs when light reflects from the top and bottom surfaces of a thin film.

thin film interference examples

• Soap bubbles

• Oil on water

thin film interference color depends on

• thickness

• wavelength

• phase shifts during reflection

Single Slit Diffraction

• Light bends around one narrow opening

• dark fringes satisfy

• asinθ=mλ

• width of central maximum= 2Lλ​ / a

• smaller slit → wider diffraction pattern

Ray Optics

Treat light as rays instead of waves.

Law of Reflection

θi​=θr​

• Incident angle equals reflected angle

Plane Mirror produces image that is

• upright

• virtual

• same size

• same distance behind the mirror as the object is in front

Refraction

Light bends because it changes speed.

Index of Refraction formula

n = c/v

• higher index (n) → lower speed

Snell's Law

n1​sinθ1​=n2​sinθ2​

• higher index → bends toward normal

• entering lower index → bends away from normal

Total Internal Reflection

Occurs only when

• light travels from higher n to lower n

• angle exceeds critical angle

total internal reflection formula

θc​=sin⁻¹(n2/n1​​)

total internal reflection examples

• fiber optics

• diamonds

a lens refracts

light

Converging Lens

• Also called convex.

• Thicker in middle.

• Parallel rays meet at focal point.

• Can produce:

  • real images

  • virtual images

Diverging Lens

• Also called concave.

• Thinner in middle.

• Always forms

  • virtual

  • upright

  • smaller images

Thin Lens Equation 1s+1s′=1f\frac1s+\frac1{s'}=\frac1f

1/s​+1/s′​=1/f​

where

• s = object distance

• s' = image distance

• f = focal length

if magnification is positive

upright image

if magnification is negative

inverted

Convex Mirror are always

• virtual

• upright

• reduced

concave mirrors can make

• real

• inverted

or

• virtual

• upright

cameras use a

converging lens

• produce real or inverted

• image on sensor or film

Human Eye

• The retina acts like a screen.

• The lens changes shape to focus.

Myopia

nearsightedness

Myopia (Nearsightedness)

• See nearby objects clearly.

• Far objects blurry.

• Corrected using

• Diverging lens

Hyperopia

farsightedness

Hyperopia (Farsightedness)

• Far objects clear.

• Near objects blurry.

• Corrected using

• Converging lens

Microscope uses

• objective lens

• eyepiece

• Total magnification: M=M_oM_e

telescope uses

• large objective lens

• eyepiece

angular magnification (telescope)

M=−f_o / f_e