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(B) The apparent frequency $f$ of sound reflected from a car moving towards a stationary source with speed $v_c$ is given by $f = f_0 \left( \frac{v +

Vedclass · Accepted Answer

$7$

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(B) The apparent frequency $f$ of sound reflected from a car moving towards a stationary source with speed $v_c$ is given by $f = f_0 \left( \frac{v + v_c}{v - v_c} ight)$.Since $v_c \ll v$,we use the binomial approximation: $f \approx f_0 \left( 1 + \frac{2v_c}{v} ight)$.The reflected frequency shift is $\Delta f = f - f_0 = f_0 \left( \frac{2v_c}{v} ight)$.For two cars with speeds $v_1$ and $v_2$,the difference in reflected frequencies is $\Delta f_{diff} = |f_1 - f_2| = f_0 \left( \frac{2(v_1 - v_2)}{v} ight)$.Given $\frac{\Delta f_{diff}}{f_0} = 1.2\% = 0.012$,we have $\frac{2(v_1 - v_2)}{v} = 0.012$.Substituting $v = 330 \ m/s$,we get $v_1 - v_2 = \frac{0.012 	imes 330}{2} = 0.006 	imes 330 = 1.98 \ m/s$.Converting to $km/h$: $1.98 \ m/s 	imes \frac{18}{5} = 7.128 \ km/h$.Rounding to the nearest integer,the difference is $7 \ km/h$.

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