Mahi Tuatahi ^🔗

Glue in and complete the beats explanation cloze activity.

Recall: Doppler Shift ^🔗

• A change in wave frequency due to the motion of emitter or observer
• Moving towards gives a higher frequency, and away a lower frequency

Beats Caused by Doppler ^🔗

• Because movement of a sound source can cause a change of frequency (Doppler effect), this can cause beats to occur.
• For example, two identical devices where one is moving towards/away from the other can cause a slight change in frequency, causing beats to arise.

Pātai Toru ^🔗

Both Josh and Zak are holding identical devices emitting a frequency of $100Hz$. Josh sprints away from him again while Zak listens. Zak observes a beat frequency of $3Hz$. The speed of sound is $343ms^{-1}$.

SHOW that Josh is walking at a speed of $v{s} = 10.6ms^{-1}$._

Step 1: Calculate $f’$ that Zak is observing from Josh’s device ($f_{b} = |f_{2} - f_{1}|$)

Step 2: Use this value to find $v_{s}$ in $f’ = f\frac{v_{w}}{v_{w} \pm v_{s}}$

Whakatika Toru a) ^🔗

$$ \begin{aligned} f_{b} &= |f_{2} - f_{1}| \newline f &= 103 \text{ or } 97 \end{aligned} $$

Because Josh is sprinting away, the frequency should be lower, so $97Hz$.

Whakatika Toru b) ^🔗

$$ \begin{aligned} f’ &= f \frac{v_{w}}{v_{w} \pm v_{s}} \text{(+ because away)} \newline 97 &= 100 \frac{343}{343 + v_{s}} \newline \frac{97}{100} &= \frac{343}{343 + v_{s}} \newline (343 + v_{s}) \times 0.97 &= 343 \newline 343 + v_{s} &= \frac{343}{0.97} \newline v_{s} &= \frac{343}{0.97} - 343 = 10.6ms^{-1} \end{aligned} $$

Practice ^🔗

1. Homework Booklet Doppler Q8c