Notes on Waves, Sounds, and Physical Optics

Unit 14: Waves, Sounds, Physical Optics

14.1 Properties of Wave Pulses and Waves

  • Types of Waves:

    • Longitudinal Waves: Motion is parallel to energy propagation; energy transmits through compression. (Example: Sound waves)

    • Transversal Waves: Motion is perpendicular to energy propagation; energy transmits through oscillations. (Example: Springs, Electromagnetic Waves)

  • Wave Properties:

    • Wave Cycle: Determined by motion of 4 wave amplitudes which include:

    • Crest

    • Trough

    • Wavelength

    • Amplitude

Investigating the Speed of Sound

  • Experiment Steps:

    • One person stands far away and claps.

    • Start timer upon seeing the clap; stop upon hearing it.

    • Measure the distance to calculate speed.

  • Equations:

    • Linear density ( m ) - mass (kg)

    • Length ( L ) - length (m)

    • Tension ( FT ) - tension (N)

    • Speed ( v ) - speed (m/s)

  • Key Point: Properties of the wave itself do not influence speed, but the properties of the medium do.

14.2 Periodic Waves

  • Frequency: Number of cycles per second; can represent pitch.

    • ( f = \frac{1}{T} )

    • Units: Hertz (Hz) or ( 1/s )

  • Modeling Waves:

    • As a function of time: ( Y = A sin \left( \frac{2\pi X}{T} \right) )

    • As a function of distance: ( Y = A sin \left( \frac{2\pi}{\lambda} X \right) )

14.5 Doppler Effect

  • Definition: Describes the effect of relative motion on observed frequency.

    • Cases:

    • Source stationary, observer moves: frequency detected equals rest frequency.

    • Source moving away: observed frequency lower.

    • Source moving towards: observed frequency higher.

14.6 Wave Interference

  • Superposition Principle: Wave interaction leads to wave interference.

    • Constructive Interference: Waves combine to create a larger amplitude.

    • Destructive Interference: Waves combine to create a smaller amplitude.

  • Beat Frequency Formula:

    • Frequency of beat = |f1 - f2|

14.3 Boundary Behavior of Waves

  • Reflection:

    • Waves into denser medium (or fixed end) invert at reflection.

    • Waves into less dense medium (or free end) reflect upright.

14.6 Resonance and Harmonics

  • Standing Waves: Created through interference of waves in a medium; characterized by nodes and antinodes.

    • Fundamental Wave (1st Harmonic): Longest wavelength, base frequency.

    • Higher Harmonics: Subsequent waves with shorter wavelengths.

14.9 Thin-Film Interference

  • Light interactions create color patterns due to interference.

    • Phase shift occurs when light reflects between different mediums with varying refractive indices.

  • Constructive Interference Conditions:

    • When light paths differ by integer multiples of the wavelength.

Diffraction

  • Definition: Spreading of waves around edges or through openings.

    • Most pronounced when opening size is comparable to the wavelength.

14.8 Double-Slit and Diffraction Grating

  • Interference Pattern: Created by two slits leads to an array of bright and dark fringes.

  • Diffraction Grating: Produces intricate interference patterns resulting in dispersion of light into its component colors.

Refraction, Reflection, and Absorption

  • Key Concepts:

    • Snell's Law: Describes refraction based on indices of refraction of involved mediums.

    • Changes in light speed and wavelength upon entering a new medium affect its path.

  • Critical Angle: Angle beyond which total internal reflection occurs.

Relevant Equations for Unit 14: Waves, Sounds, Physical Optics

  • Speed of Sound Equation:
    v = \frac{d}{t}
    (Where d = distance, t = time)

  • Frequency and Period Relationship:
    f = \frac{1}{T}
    (Where f = frequency in Hz, T = period in seconds)

  • Modeling Waves as a Function of Time:
    Y = A \sin \left( \frac{2\pi X}{T} \right)
    (Where Y = wave function, A = amplitude, X = distance, T = period)

  • Modeling Waves as a Function of Distance:
    Y = A \sin \left( \frac{2\pi}{\lambda} X \right)
    (Where \lambda = wavelength)

  • Beat Frequency Formula:
    Frequency of beat = | f1 - f2 |
    (Where f1 and f2 are the frequencies of two waves)

  • Snell's Law for Refraction:
    n1 \sin(\theta1) = n2 \sin(\theta2)
    (Where n = index of refraction, \theta = angle of incidence or refraction)

  • Critical Angle:
    \sin(\thetac) = \frac{n2}{n1} (Where \thetac = critical