Question

Consider a source of sound S, and an observer/detector D. The source emits a sound wave of frequency $f_0$. The frequency observed by D is found to be

• A. $f_1\ne f_2\ne f_3$
• B. $f_1<f_2$
• C. $f_3<f_0$
• D. $f_1<f_3<f_2$

Answer 1

The correct option is C $f_3<f_0$

Let relative velocity be v and the speed sound be $v_0$. Then,
$f_1=\frac{v_0-(-v)}{v_0}\times f_0=\frac{v_0+v}{v_0}{f}_0{f}_2=\frac{v_0}{v_0-v}\times f_0{f}_3=\frac{v_0+\frac{v}{2}}{v_0-\frac{v}{2}}\times f_0$
It is clear from above that $f_1\ne f_2\ne f_3,f_3>f_0$ and we can prove that $f_2>f_3>f_1$.