Question

The equation of the progressive wave, where t is the time in second, x is the distance in metre is $y=Acos240(t-\frac{x}{12})$. The phase difference (in SI units) between two positions$0.5m$ apart is

• A. $40$
• B. $20$
• C. $10$
• D. $5$

Answer 1

The correct option is C $10$

Given$:$

Time $=ts$

Distance $=xm$

$y=Acos240(t-x/12)$

Distance $=0.5m$

$y=A\cos 240\left(\frac{240t-240x}{12}\right)$

To find the wavelength$,$

$k=240/12$

$k=20$

$k$ is Wave number$.$

$\lambda =2\pi /20$

$\lambda$ is the wavelength$.$

$0.5/\lambda =\theta /2\pi$

$0.5/\left(2\pi /20\right)=\theta /2\pi$

$\theta ={10}^0$

The phase difference between two positions $0.5m$ apart is ${10}^0$

Hence,

option $\left(C\right)$ is correct answer.