Question

Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an approaching ambulance, After the ambulance passes, the observed frequency of the siren is 480 Hz. Determine the ambulance's speed from these observations. Speed of sound =343(m)/(s).

Answer 1

Answer:

In this kind of questions , do apply Doppler's Effect equation in 2 parts :

• Before the observer
• After the observer

When ambulance was approaching observer :

$f1 = \bigg\{ \dfrac{v - v_{o}}{v - v_{s}} \bigg \}f$

$= > 560 = \bigg\{ \dfrac{343 - 0}{343 - v} \bigg \}f$

When ambulance is going away from the observer :

$f1 = \bigg\{ \dfrac{v - v_{o}}{v + v_{s}} \bigg \}f$

$= > 480= \bigg\{ \dfrac{343 - 0}{343 + v} \bigg \}f$

Dividing the 2 Equations , we get that :

$= > \dfrac{560}{480} = \dfrac{343 + v}{343 - v}$

$= > \dfrac{7}{6} = \dfrac{343 + v}{343 - v}$

$= > 2401 - 7v = 2058 + 6v$

$= > 13v = 343$

$= > v = 26.38 \: m {s}^{ - 1}$

So final answer :

$\boxed{ \sf{ \huge{ \red{ v = 26.38 \: m {s}^{ - 1}}}}}$