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 $t = 0$ ?

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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 $t = 0$ ?

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 $Q$ .