Question

If a source emitting waves of frequency $f$ moves towards an observer with a velocity $\frac{v}{4}$ and the observer moves away from the source with a velocity $v/6$, the apparent frequency as heard by the observer will be ($v=$ velocity of sound)

• A. $\frac{14}{15}f$
• B. $\frac{14}{9}f$
• C. $\frac{10}{9}f$
• D. $\frac{2}{3}f$

Answer 1

The correct option is C $\frac{10}{9}f$

When source and observer both are moving in the same direction and observer is ahead of source, then apparent frequency
$f^{\prime }=\frac{v-v_0}{v-v_s}f$
$=\frac{v-\frac{v}{6}}{v-\frac{v}{4}}=\frac{\frac{5v}{6}}{\frac{3v}{4}}f=\frac{10}{9}f$