Question

If y= A sin(wt-kx) then the value of {dy/dx}/{dy/dt}is

Answer 1

∴ The correct answer is  {dy/dx}/{dy/dt} = -k/w

Given:

y= A sin(wt - kx)

To Find:

The value of {dy/dx}/{dy/dt}.

Solution:

To solve this problem we will use the following concepts:

1. d/dx sinx = cos x
2. If u = t$o$ v is the function that is given by h(x) = f(g(x)), then

          u'(x) = t'(v(x)). v'(x)

We have been given that y = A sin(wt - kx)

dy/dx = A cos(wt - kx) × d/dx( wt - kx) =  -Ak cos(wt - kx)

dy/dt = A cos(wt - kx) × d/dt( wt - kx) = Aw cos(wt - kx)

Now,

{dy/dx}/{dy/dt} = (-Ak cos(wt - kx) )/( Aw cos(wt - kx) ) = -k/w

∴ {dy/dx}/{dy/dt} = -k/w

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