Question

Two points on a traveling wave having a frequency $600Hz$ and velocity $300\frac{m}{s}$ are $60°$ out of phase, then the minimum distance between the two points is

• A. $0.3$
• B. $0.083$
• C. $0.25$
• D. $0.4$

Answer 1

The correct option is B

$0.083$

Step 1: Given data

The frequency of the wave is $600Hz$

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

The phase difference of the wave is $60°$

Step 2: Calculation

The relation of the frequency with a wavelength

$$\begin{gathered} v=\lambda n \\ here \\ v=velocityofwave \\ \lambda =wavelengthofthewave \\ n=frequencyofthewave \end{gathered}$$

$$\begin{gathered} \Rightarrow \lambda =\frac{v}{n} \\ \Rightarrow \lambda =\frac{300}{600} \\ \Rightarrow \lambda =\frac{1}{2}m..........\left(1\right) \end{gathered}$$

Now, the relation of the phase difference with the path difference,

$Phasedifference=\frac{2\mathrm{\pi }}{\lambda }\times Pathdifference$

$$\begin{gathered} \Rightarrow 60°=\frac{2\mathrm{\pi }}{\lambda }\times Pathdifference \\ \Rightarrow 60°=\frac{2\mathrm{\pi }}{\left({\displaystyle \frac{1}{2}}\right)}\times Pathdifference..........(From1) \\ \Rightarrow Pathdifference=\frac{60°}{4\mathrm{\pi }}=0.083m \end{gathered}$$

Hence, the correct option is $B$.