Consider the equation y ( x , t ) = A cos( at ) sin( bx ) Let x represent some p

Question

Consider the equation

y(x, t) =A cos(at) sin(bx)

Let x represent some position and t represent time.

Describe a physical situation that could be represented by this equation. As part of your description include a sketch and a written description.

Indicate what y and x correspond to in the situation you describe.<_>

How, if at all, would the physical situation you described in part A be different if a were twice as large? Explain how you determined your answer.

How, if at all, would the physical situation you described in part A be different if b were twice as large? Explain how you determined your answer.

Explanation / Answer

here it is the expression of standing wave

here y is the particle displacement along the string

x is the wave propagation's position long the x axis

here a is the w = 2pif

is a is double then frequency of the wave becoes double

if b is double that is here b = k = propagation constant

if b double k is also double that is wave length is reduced by 1/2 times

k = 2pi/wavelength

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