Max speed perpendicular to the wave's direction

[Bsky]

Homework Statement

This question is part of a longer problem. I know the answer, but I don't know how they got their. Please provide a detailed explanation. Thanks.

Question: Find the maximum speed perpendicular to the wave's direction of travel (the transverse speed).

y(x,t)=2sin(4x-2t)

Homework Equations

The book gives a hint: find amplitude of dy/dt. Therefore, dy/dt=2cos(4x-2t)

The Attempt at a Solution

Period= pi
Lambda= pi/2
Frequency= 1/pi
v=1/2

 

[kuruman]

y(x,t)=2sin(4x-2t)

Homework Equations

The book gives a hint: find amplitude of dy/dt. Therefore, dy/dt=2cos(4x-2t)

Incorrect. You forgot to apply the chain rule of differentiation.

 

[Swap]

here u have to take x=0 as u r considering the perpendicular velocity. So once u assume that differentiate it and then u will get the max. value