AP Physics 2 - Waves

Waves

  • A periodic disturbance that transfers energy (DO WORK) without the transfer of matter

  • transfer energy between two locations without transferring matter between those locations

  • composed of multiple pulses

    • Wave Pulse

      • single disturbance that transfers energy without transferring matter

  • move by propagating

    • each small section of the wave causes the next small section to move

Mechanical Waves

  • Require a medium

    • material in which to propagate

      • air, water, spring

    • Waves on a rope

    • Water waves

    • Sound waves

  • Transverse

  • Longitudinal

  • Surface


Electromagnetic Waves

  • Don’t require a medium

    • Can move through different media

  • Difficult to observe

    • Radio waves

    • Microwaves

    • Infrared waves

    • Ultraviolet waves

    • X rays

    • Gamma waves

    • Light

  • Transverse


Matter Waves

  • Electrons and other particles show wave like behaviors under certain circumstances

  • Quantum Mechanics is needed to describe waves

Longitudinal Waves

  • Mechanical and electromagnetic

  • motion of medium is parallel to propagation of wave

  • Dense Parts = Compressions

    • High Pressure

  • Spread out parts = Rarefactions

    • Low Pressure

Transverse Wave

  • motion of medium is perpendicular to propagation of wave

  • High Point = Crest

  • Low Point = Trough

  • Amplitude

    • Energy in the wave

Surface Waves

  • Mix of transverse and longitudinal

  • Travels along the surface or interface between two media

    • Waves in a pool

Speed of a Wave

  • depends on medium and type of wave moving through

  • Velocity = ΔX / Δt

  • Same pulse but different amplitude = same velocity

    • Amplitude doesn’t affect velocity

      • Amplitude = maximum displacement of wave from equilibrium position

  • Different pulse but same amplitude = same velocity

    • Pulse width doesn’t affect velocity

  • Linear Density = mass of string / length

  • Speed of Wave on string/spring

    • Depends on Tension

      • Direct Root

    • Depends on Linear Density

      • Indirect Root

    • Velocity = √FT / √μd

      • μd = m / L

      • λ = v / f

        • Wavelength

  • Sound waves

    • 343 m/s at 20 degrees Celsius

      • For every 1 degree speed increases .6 m/s

Waves at Boundaries

  • Every incoming wave (incident wave) becomes two waves when it strikes a boundary

    • Transmitted (refracted)

      • Wave that travels into the new medium

    • Reflected

      • Wave that bounces back from the medium

Reflected Wave

  • How much is reflected depends on the medium

    • If the wave hits a more rigid medium, reflected Amplitude (energy) is large but inverted

    • If the wave hits a less rigid medium, reflected Amplitude (energy) is small and upright

Transmitted Wave

  • How much is transmitted depends on the medium

    • If the two media are similar, transmitted Amplitude (energy) is large

    • If the two media are very different, transmitted Amplitude (energy) is small

Wave Behavior

  • Reflection of waves

    • The Law of Reflection

      • The angle of incidence is equal to the angle of reflection

        • θi = θf

      • The incident ray, reflected ray, and normal all must be in the same plane (all 2D)

  • Refraction of waves

    • The change in the direction of waves at the boundary between two different media

    • Bending

    • V2sinθ1 = V1sinθ2

  • Diffraction

    • The spreading of waves around the edge of a barrier

    • The amount of diffraction depends on the size of the obstacle compared to the wavelength

      • If the obstacle is much smaller than the wavelength, the wave is barely affected

      • If the object is comparable to, or larger than, the wavelength, diffraction is much more significant

  • Interference

    • Two waves can combine to form a new wave

    • Principle of Superposition

      • The displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by the individual waves

      • Constructive Interference

        • Add together

        • Mechanical Resonance

      • Destructive Interference

        • Cancel

Standing Waves

  • Occur when both ends of a string are fixed

    • Only waves which are motionless at the ends of the string can persist

    • Nodes

      • Amplitude is always zero

      • Segment (n)

        • Distance between nodes

    • Antinodes

      • Amplitude varies from zero to max value

  • Resonant Frequencies

    • Frequencies of standing waves on a particular string

    • Fundamental / Harmonics

      • Overtones

Sound Waves

  • Pressure waves in solids, liquids, and gases

    • Hit the eardrum and are converted to nerve impulses, which are interpreted as sound

  • Longitudinal wave

    • MAY have transverse components in solids

  • Ultrasonic waves are too high in frequency for human ears

    • Ultrasound

      • Echolocation

      • Commercial / medical

  • Human range = 20 Hz → 20kHz

  • Infrasonic waves have frequencies too low for human ears

  • Pitch = Frequency

  • Speed of Sound

    • Speed in dry air

      • (331 + 0.6TC) m/s

      • depends on temperature

  • Intensity

    • Power per unit area

    • I = (E/t) / A = P / A

    • Inversely proportional to square of distance from point source

    • Minimum Detectable sound

      • 1.0 × 10-12 W/m2

    • Threshold of pain

      • Starts at 1.0 W/m2

    • doubling of loudness corresponds to increase in intensity of ~10x

    • Decibel Scale

      • β = 10log ( I / I0 )

      • 0 threshold of hearing

      • 60 normal conversation

      • 90 Subway train

        • Exposure over for long time could affect hearing

      • 110 Concert

        • Threshold of pain

      • 180 Rocket launch

Sources of Sound

  • Musical instruments

    • vibrating strings, vibrating membranes, vibrating metal/wood, vibrating air columns

    • Vibration started by plucking, striking, bowing, or blowing

    • Guitar

      • “Shortened” by fingering

      • Different densities

    • Piano

      • Lower strings are much longer and much thicker

  • Air Columns

    • Wind instruments

    • Open Pipe Resonator

      • Both ends open

      • Antinode at both ends

    • Closed Pipe Resonator

      • Only one end open

      • Antinode at open end, node at closed end

      • f = (nV) / (4L)

      • Intervals are odd integer values

Doppler Effect

  • Apparent change in frequency as a result of moving observer or moving source

  • The Doppler effect occurs when a source of sound is moving with respect to an observer

    • Sound waves are more condensed in the direction of the objects velocity

  • Source frequency never changes

    • Perceived frequency changed

Sound Phenomena

  • Reflection

    • “bouncing” of sound waves off a surface

  • Refraction

    • “bending” of sound waves as they pass through a varying medium

  • Diffraction

    • “bending” of sound waves around an obstacle or opening

  • Interference

    • Occurs when multiple waves propagate through the same medium

    • Either constructive or destructive