Question

Two points on a traveling wave having frequency $500Hz$ and velocity $300\frac{m}{s}$ are $60°$ out of phase, then the minimum distance between the two points is

• A. $0.2$
• B. $0.1$
• C. $0.4$
• D. $0.5$

Answer 1

The correct option is B

$0.1$

Step 1: Given

The frequency of the wave is $500Hz$.

The velocity of the point is $300\frac{m}{s}$.

The phase difference of the wave is $60°$.

Step 2: Solution

Let the velocity of the particle be $v$

So, Velocity$=$Frequency$\left(n\right)$$\times$Wavelength$\left(\lambda \right)$

$$\begin{gathered} \Rightarrow \lambda =\frac{v}{n} \\ \Rightarrow \lambda =\frac{300}{500} \\ \Rightarrow \lambda =\frac{3}{5}m \end{gathered}$$

Now, the phase difference$=\frac{2\mathrm{\pi }}{\lambda }\times Pathdifference$

$\Rightarrow 60°=\frac{2\mathrm{\pi }}{\left({\displaystyle \frac{3}{5}}\right)}\times Pathdifference$

$$\begin{gathered} \Rightarrow Pathdifference=\frac{180°}{1800°} \\ \Rightarrow Pathdifference=0.1° \end{gathered}$$

Hence, the correct option is $B$.