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

• Textbook Activity 6A Q3
• P3.3 Worksheet #4 Q3a
• Homework Booklet Q7