Question

The standing wave in a medium is expressed as $y=0.2\sin \left(0.8x\right)\cos \left(3000t\right)\text{m}$. The seperation between any two consecutive points of minimum or maximum displacement is

• A. $\frac{\pi }{2}\text{m}$
• B. $\frac{\pi }{4}\text{m}$
• C. $\frac{\pi }{6}\text{m}$
• D. $\frac{5\pi }{8}\text{m}$

Answer 1

The correct option is D $\frac{5\pi }{8}\text{m}$

Given,
Equation of a stationary wave,
$y=0.2\sin \left(0.8x\right)\cos \left(3000t\right)$

Comparing this with

$y=2A\sin \left(\frac{2\pi x}{\lambda }\right)\cos \left(\frac{2\pi t}{T}\right)$
we get, $\lambda =\frac{2\pi }{0.8}$

The seperation between any two points of minimum and maximum displacement is ${\left(\frac{1}{4}\right)}^{th}$ of the total wavelength.
$\Delta x=\frac{\lambda }{4}=\frac{5\pi }{8}\text{m}$