Question

A sound wave is represented by $y=a\sin (1000\pi t-3x)$. The distance between two points having a phase difference of $\frac{\pi }{3}$ is

• A. $\frac{5\pi }{18}$
• B. $\frac{2\pi }{9}$
• C. $\frac{\pi }{18}$
• D. $\frac{\pi }{9}$

Answer 1

Answer: (D)

$\frac{\pi }{9}$

Given equation - $y=a\sin (100\pi t-3x)$ ,

by comparing this equation with , $y=a\sin (\frac{2\pi t}{T}-\frac{2\pi x}{\lambda })$ ,

we get , $2\pi x/\lambda =3x$ ,

or $\lambda =2\pi /3$ ,

now given , phase difference , $\Delta \varphi =\pi /3$ ,

therefore path difference (distance between two points) will be ,

$\Delta x=\lambda /2\pi \times \Delta \varphi$ ,

or $\Delta x=\left(2\pi /3\right)/2\pi \times \pi /3=\pi /9$ ,