# Question 264d2

May 6, 2017

$735 \text{ Hz}$

#### Explanation:

This question tests you on your understanding of the $\text{Doppler effect}$. The phenomenon occurs when the observer, the one listening, and the source, the one producing the sound, are moving away or toward each other.

The $\text{Doppler effect}$ occurs when there is a change in relative motion of the source or observer. This in turn changes the distance traveled by the wave fronts of the sound. This in turn changes the observed frequency . The actual frequency, though, does not change. Basic rules:

• If the observer or the source is standing still, or not moving, its speed is taken to be $0 \text{ m/s}$.

• If the observer is moving toward the source, the (+) sign is used, if observer is moving away, the (-) sign is used

• If the source is moving toward the observer, the (-) sign is used, if source is moving away, the (+) sign is used.

The equation to use to solve this problem is,

color(white)(aaaaaaaaaaaaaaaa)color(magenta)(f_(o) = f_(s)[(v+-v_(o))/(v+-v_(s))]#

Where
${f}_{o} = \text{observed frequency}$
${f}_{s} = \text{frequency of the source}$
$v = \text{speed of sound}$
${v}_{o} = \text{speed of observer}$
${v}_{s} = \text{speed of source}$

${f}_{o} = {f}_{s} \left[\frac{v \pm {v}_{o}}{v \pm {v}_{s}}\right] \to {f}_{o} = 700 \left(\frac{343 + 0}{343 - 15}\right) \to 700 \left(\frac{343}{328}\right) \to 700 \cdot 1.05 \to \textcolor{b l u e}{735 \text{ Hz}}$

This answer actually makes sense because if you have even stood still and heard an ambulance or firetruck approaching you, the frequency of the sound which you observe of the trucks seems to be higher (its pitch). This is exactly what is going on in this problem.