Question

A simple harmonic wave of amplitude 2 units is travelling along positive x – axis. At a given instant,displacement for two different particles on the wave are 1 unit and $\sqrt{2}$ unit. If the wavelength of wave is $\lambda$, find the distance between them.

• A. $\frac{\lambda }{12}$
• B. $\frac{\lambda }{8}$
• C. $\frac{\lambda }{24}$
• D. $\frac{\lambda }{16}$

Answer 1

The correct option is C $\frac{\lambda }{24}$

$\frac{\lambda }{A}=sin2\pi (\frac{t}{T}-\frac{x}{\lambda })y_1=1,A=2,2\pi (\frac{t}{T}-\frac{X-2}{\lambda })=si{n}^{-1}\left(\frac{1}{2}\right)=\frac{\pi }{16}rad{y}_1=\sqrt{2},A=2,2\pi (\frac{t}{T}-\frac{X_2}{\lambda })=si{n}^{-1}\left(\frac{1}{\sqrt{2}}\right)=\frac{\pi }{4}rad\frac{t}{T}-\frac{x_1}{\lambda }=\frac{1}{12};\frac{t}{T}-\frac{x_2}{\lambda }=\frac{1}{8}Substract,\frac{x_1}{\lambda }-\frac{x_2}{\lambda }=\frac{1}{24};(x_1-x_2)=\frac{\lambda }{24}$