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Doppler Wave Velocity

Mahi Tuatahi 🔗

Y12 Textbook Activity 5B: Reflection, Refraction and Diffraction of Waves Q5

Hint: Look on the previous pages.

Doppler Skill 3: Finding $v_{w}$ 🔗

$$ \begin{aligned} & f’ = f\frac{v_{w}}{v_{w} \pm v_{s}} \end{aligned} $$

  1. Identify when you are in a $+$ or a $-$ situtation,
  2. Substitute your knowns,
  3. Simplify and re-arrange to solve.

Pātai: 52-hertz Whale 🔗

Since the 1980s a single whale has been observed making calls at a frequency of $52Hz$. The whale itself has never been sighted – only observed through hydrophones. One hydrophone recorded a frequency of $52.1171762Hz$.

This recording has been sped up 10x to a frequency of approximately $520Hz$.

  1. Was the whale moving towards or away from the hydrophone? Justify your answer.
  2. Calculate the speed of sound in the water, given a whale feeding speed of approximately $3.35ms^{-1}$

Whakatika 🔗

$$ \begin{aligned} f&=52Hz, f’=52.1171762Hz, v_{s}=3.35ms^{-1} \newline f’ &= f \frac{v_{w}}{v_{w} - v_{s}} \newline 52.1171762 &= 52 \frac{v_{w}}{v_{w} - 3.35} \newline 1.0022534 \times (v_{w} - 3.35) &= v_{w} \newline 1.0022534v_{w} - 3.35754889 &= v_{w} \newline 1.0022534v_{w} - v_{w} &= 3.35754889 \newline v_{w}(1.0022534 - 1) &= 3.35754889 \newline v_{w} &= \frac{3.35754889}{0.0022534} = 1489.99ms^{-1} \end{aligned} $$

Practice 🔗