Question

A bird is singing on a tree and a man is hearing at a distance ${}^{\prime }{r}^{\prime }$ from the bird. Calculate the displacement of the man towards the bird so that the loudness heard by man increases by $20dB$.
[Assume that the motion of man is along the line joining the bird and the man]

• A. $\frac{9r}{10}$
• B. $\frac{r}{10}$
• C. $\frac{3r}{5}$
• D. $\frac{4r}{5}$

Answer 1

The correct option is A $\frac{9r}{10}$

Loudness $\beta =10lo{g}_{10}\frac{I}{I_0}$

$\therefore {\beta }_2-{\beta }_1=10lo{g}_{10}\frac{I_2}{I_1}$

$\because I=\frac{P}{4\pi r^2}\therefore \frac{I_2}{I_1}=\frac{r_1^2}{r_2^2}$

$\therefore (\beta +20)-\beta =10lo{g}_{10}\frac{r^2}{r_2^2}=20lo{g}_{10}\frac{r}{r_2}$

$\Rightarrow \frac{r}{r_2}=10\Rightarrow r_2=0.1r$

$\therefore shift=r-0.1r=0.9r$.