# Chapter 12 - Problems - Page 465: 50

The speed of the race car is $49.0~m/s$

#### Work Step by Step

Let $v_c$ be the race car's speed. We can use the equation for the Doppler effect when the observer is approaching to find an expression for the higher frequency $f_h$: $f_h = \left(\frac{v+v_c}{v}\right)~f_s$ We can use the equation for the Doppler effect when the observer is moving away to find an expression for the lower frequency $f_l$: $f_l = \left(\frac{v-v_c}{v}\right)~f_s$ Note that $f_l = 0.75~f_h$: $f_l = 0.75~f_h$ $\left(\frac{v-v_c}{v}\right)~f_s = 0.75~\left(\frac{v+v_c}{v}\right)~f_s$ $v-v_c =0.75~(v+v_c)$ $1.75~v_c = 0.25~v$ $v_c = \frac{0.25~v}{1.75}$ $v_c = \frac{(0.25)~(343~m/s)}{1.75}$ $v_c = 49.0~m/s$ The speed of the race car is $49.0~m/s$.

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