Question

Two points are located at a distance of 10 m and15 m from the source of oscillation. The period of oscillation is 0.05 sec and the velocity of the
wave is 300 m/s. What is the phase difference between the oscillations of two points?

• A. $\pi$
• B. $\pi /6$
• C. $\pi /3$
• D. $2\pi /3$

Answer 1

The correct option is D $2\pi /3$

$\text{Given:-}$ Two points are located at a distance of 10m and 15m

The period of oscillation = 0.05s

The velocity of the wave = 300m/s

$\text{To find:-}$ The phase difference between the oscillation of two points.

$\text{Solution:-}$ We know that,

Path difference = $\frac{2\pi }{\lambda }\times pathdifference$

Path difference between two points,

$\Delta x=15-10=5m$

Time period, T = 0.5s

$\Rightarrow frequencyv=\frac{1}{T}=\frac{1}{0.05}=20Hz$

Velocity v = 300m/s

$\therefore Wavelenght\lambda =\frac{v}{n}=\frac{300}{20}=15m$

Hence, phase difference

$\Delta \varphi =\frac{2\pi }{\lambda }\times x=\frac{2\pi }{15}\times 5=\frac{2\pi }{3}$

$\text{Hence the correct option is D}$