Waves

Last updated Jun 15, 2023 Edit Source

# ← Physics Home

• $I = \frac{P}{A}$
  • Measured in watts per metre squared (or decibels)
    • $W m^{-2}$ or dB
  • $I \propto \frac{1}{r^2}$
    • Intensity is inversely related to $\frac{1}{r^2}$
  • Amplitude decreases over time because the energy is spread over a larger area
    • Not just because energy is lost from the system
  • Example Question:
    • An ornithologist is watching a noisy scrub bird building its mound from a ‘hide’ which is $86.3 m$ from the mound. The ornithologist drops their binoculars which startles the bird, which commences screeching at an intensity of $2.38 * 10^{-5}\\ W \\ m^{-2}$ as measured by the ornithologist. The bird also starts running away from the hide. How far away will it be from the hide by the time the screech has an intensity of $4.73 * 10^{-6} \\ W \\ m^{-2}$?
      • Find given variables:
        1. $I_i = 2.38 * 10^{-5}\\ W \\ m^{-2}$
        2. $I_f = 4.73 * 10^{-6}\\ W \\ m^{-2}$
        3. $r_i = 86.3m$
      • Input into formula:
        1. $\frac{I_i}{I_f} = \frac{2.38\\ *\\ 10^{-5}}{4.73\\ *\\ 10^{-6}} = 5.03$
        2. $\frac{I_i}{I_f} = \frac{{r_f}^2}{{r_i}^2} = (\frac{r_f}{r_i})^2 = 5.03$
      • Solve:
        1. $\frac{r_f}{r_i} = \sqrt{5.03}$
        2. $\therefore\\ r_f \\ = \\ r_i * \sqrt{5.03} \\ = \\ 86.3 * \sqrt{5.03} \\ = \\ 194m$