Question #161989

Standing at a crosswalk, you hear a frequency of 560Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 480Hz. Determine the ambulance speed from these observations.

(V = 340m/s)


1
Expert's answer
2021-02-22T16:04:59-0500

Initially, the ambulance approaching the person, so we can write:


f1=f(vvvs).f_1=f(\dfrac{v}{v-v_s}).

Then, the ambulance moves away from the person, therefore, we can write:


f2=f(vv+vs).f_2=f(\dfrac{v}{v+v_s}).

Let's divide the first eqution by the second one, we get:


f1f2=v+vsvvs,\dfrac{f_1}{f_2}=\dfrac{v+v_s}{v-v_s},560480=v+vsvvs,\dfrac{560}{480}=\dfrac{v+v_s}{v-v_s},480(v+vs)=560(vvs),480(v+v_s)=560(v-v_s),80v=1040vs,80v=1040v_s,vs=80v1040=80340 ms1040=26.15 ms.v_s=\dfrac{80v}{1040}=\dfrac{80\cdot340\ \dfrac{m}{s}}{1040}=26.15\ \dfrac{m}{s}.

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