Question

For he transverse wave equation $y=Asin(\pi x+\pi t),$ choose the correct options at t = 0

• A. points at x = 0 and x = 1 are at mean positions
• B. points at x = 0.5 and x = 1.5 have maximum accelerations
• C. points at x = 0.5 and x = 1.5 are at rest
• D. the given wave is travelling in negative x direction

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A points at x = 0 and x = 1 are at mean positions
B points at x = 0.5 and x = 1.5 have maximum accelerations
C points at x = 0.5 and x = 1.5 are at rest
D the given wave is travelling in negative x direction

$y=Asin(\pi x+\pi t)$

At $t=0$, wave form is
$y=Asin\left(\pi x\right)$

At $x=0,1$ $⟹y=0$

Hence option A is correct.

$v=\frac{dy}{dt}=A\pi cos(\pi x+\pi t)$

At $t=0,x=0.5,1.5⟹v=0$

Hence option C is correct.

Acceleration of points=$\frac{d^{2}y}{d{t}^2}=-A{\omega }^{2}sin(\pi x+\pi t)$

At $t=0,x=0.5,1.5$, acceleration is maximum.

Hence option B is correct.

Since the wave form has positive sign between the $x$ and $t$ term, the wave is left travelling.

Hence option D is correct.