A wave motion has the function y=a0 sin (ω t-k x). The graph in figure shows how the displacement y at a fixed point varies with time t. Which one of the labelled points shows a displacement equal to that at the position x=(π/2 k) at time t=0

Question

A wave motion has the function y=a0 sin (ω t-k x). The graph in figure shows how the displacement y at a fixed point varies with time t. Which one of the labelled points shows a displacement equal to that at the position x=(π/2 k) at time t=0 (A) P (B) Q (C) R (D) S

Tardigrade Admin · Accepted Answer

At t=0 and x=(π/2 k). The displacement y=a0 sin (ω x0-k × (π/2 x))=-a0 sin (π/2)=-a0 from graph. Point of maximum displacement (a0) in negative direction is Q.

Q. A wave motion has the function $y = a_{0} sin (ω t - k x)$ . The graph in figure shows how the displacement $y$ at a fixed point varies with time $t$ . Which one of the labelled points shows a displacement equal to that at the position $x = \frac{π}{2 k}$ at time $t = 0$

$P$

$Q$

$R$

$S$

At $t = 0$ and $x = \frac{π}{2 k}$ . The displacement
$y = a_{0} sin (ω x_{0} - k \times \frac{π}{2 x}) = - a_{0} sin \frac{π}{2} = - a_{0}$
from graph. Point of maximum displacement $(a_{0})$ in negative direction is $Q$ .

Q. A wave motion has the function y=a0​sin(ωt−kx). The graph in figure shows how the displacement y at a fixed point varies with time t. Which one of the labelled points shows a displacement equal to that at the position x=2kπ​ at time t=0

P

Q

R

S

At t=0 and x=2kπ​. The displacement y=a0​sin(ωx0​−k×2xπ​)=−a0​sin2π​=−a0​ from graph. Point of maximum displacement (a0​) in negative direction is Q.

Q. A wave motion has the function $y = a_{0} sin (ω t - k x)$ . The graph in figure shows how the displacement $y$ at a fixed point varies with time $t$ . Which one of the labelled points shows a displacement equal to that at the position $x = \frac{π}{2 k}$ at time $t = 0$

$P$

$Q$

$R$

$S$

At $t = 0$ and $x = \frac{π}{2 k}$ . The displacement
$y = a_{0} sin (ω x_{0} - k \times \frac{π}{2 x}) = - a_{0} sin \frac{π}{2} = - a_{0}$
from graph. Point of maximum displacement $(a_{0})$ in negative direction is $Q$ .