Consider the equation: y ( x , t ) = A cos( at ) sin( bx ) Let x represent some
ID: 1477851 • Letter: C
Question
Consider the equation: y(x, t) =A cos(at) sin(bx)
Let x represent some position and t represent time.
A, Describe a physical situation that could be represented by this equation. Indicate what y and x correspond to in the situation you describe.
B. 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.
C. 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
A. a wave travelling along +ve x axis is represented by 0.5*A*sin(b*x-a*t)
a wave travelling along -ve x axis can be represented by 0.5*A*sin(a*t+b*x)
addition of the waves is given by 0.5*A*(sin(b*x-a*t)+sin(a*t+b*x))=2*0.5*A*cos(a*t)sin(b*x)=A*cos(a*t)sin(b*x)
this is the equation of a standing wave where t represents time, x represents distance along the axis and y represents its lateral displacement (i.e. height/depth of the wave ) at any time t and at a position x.
amplitude of the wave is A*sin(b*x).
time period=2*pi/a
wavelength=2*pi/b
part B:
if a were twice, as time period=2*pi/a, time period will be halved.
part C:
if b were twice, as wavelength=2*pi/b, wavelength will be halved.