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Wave Functions & Equations of Waves quiz #1

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Terms in this set (10)

  • How do light waves travel, and how does this differ from other types of waves?
    Light waves are unique because they can propagate through a vacuum, meaning they do not require a medium to travel. In contrast, most other types of waves, such as sound or waves on a string, require a medium (like air, water, or a solid) for propagation. The speed and behavior of these other waves depend on both the type of wave and the properties of the medium they travel through.
  • What determines whether a wave is described by a sine or cosine function?
    The initial displacement of the wave determines whether it is described by a sine (zero displacement) or cosine (maximum displacement) function. This choice reflects the wave's starting position at time zero.
  • How is the wave number (k) defined mathematically?
    The wave number k is defined as 2π divided by the wavelength (k = 2π/λ). It has units of inverse length, such as m⁻¹ or cm⁻¹.
  • What is the general form of a wave function that includes both space and time dependence?
    The general form is y = A sin(kx - ωt + φ), where A is amplitude, k is wave number, ω is angular frequency, t is time, x is position, and φ is the phase angle. This form describes oscillations in both space and time.
  • What does the phase angle (φ) in a wave function represent?
    The phase angle φ represents the initial displacement of the wave at x = 0 and t = 0. It determines how much the wave is shifted horizontally from a pure sine or cosine wave.
  • How can you determine the direction of wave propagation from its equation?
    If the argument of the wave function is (kx - ωt), the wave propagates in the positive x-direction; if it is (kx + ωt), the wave propagates in the negative x-direction. The sign in front of ωt indicates the direction.
  • What is the relationship between angular frequency (ω) and period (T)?
    Angular frequency ω is related to the period T by ω = 2π/T. This means the period is T = 2π/ω.
  • How do you find the propagation speed of a wave from its wave function parameters?
    The propagation speed v of a wave is given by v = ω/k, where ω is the angular frequency and k is the wave number. This formula applies to both transverse and longitudinal waves.
  • What is the maximum transverse velocity for a transverse wave, and how is it calculated?
    The maximum transverse velocity is given by the product of amplitude and angular frequency, Aω. It represents the fastest speed at which the medium moves perpendicular to the direction of wave propagation.
  • Why do longitudinal waves have zero transverse velocity?
    Longitudinal waves oscillate in the direction of propagation, so there is no motion perpendicular to that direction. Therefore, their transverse velocity is always zero.