Please show me step by step solution and explanation for this.Sorry if this is too much but I really need help =(
A progressing waveform along the x-axis is represented as
u(x,t) = 12 / [4 + (2x+3t+1)^4].
the unit for x and u is in m, and unit for t is seconds.
1. Find the direction of the wave and its velocity.
Hints:
The problem states "progressing waveform" and so it is the velocity of the progressing wave that must be solved. u(x,t) represents the displacement and therefore, the result of its time derivative is the velocity of what?
2. Find the amplitude of this wave.
3.From t=0 until 3 seconds later,what is the
A progressing waveform along the x-axis is represented as
u(x,t) = 12 / [4 + (2x+3t+1)^4].
the unit for x and u is in m, and unit for t is seconds.
1. Find the direction of the wave and its velocity.
Hints:
The problem states "progressing waveform" and so it is the velocity of the progressing wave that must be solved. u(x,t) represents the displacement and therefore, the result of its time derivative is the velocity of what?
2. Find the amplitude of this wave.
3.From t=0 until 3 seconds later,what is the
-
u(x,t) = 12 / [4 + (2x+3t+1)^4]
u is a maximum, when (2x + 3t + 1) = 0
so the amplitude is 12/4 = 3 m
the peak value of the wave is at those values of x, where 2x + 3t + 1 = 0 is fulfilled.
--> x = - 3/2*t - 1/2
the derivative of x with respect to time is the velocity of the peak of the wave:
v = dx/dt = - 3/2 = - 1.5 m/s
the wave progresses into the -x direction with 1.5 m/s
see 3d picture of progressing wave:
http://www.wolframalpha.com/input/?i=u%2…
3)?
OG
u is a maximum, when (2x + 3t + 1) = 0
so the amplitude is 12/4 = 3 m
the peak value of the wave is at those values of x, where 2x + 3t + 1 = 0 is fulfilled.
--> x = - 3/2*t - 1/2
the derivative of x with respect to time is the velocity of the peak of the wave:
v = dx/dt = - 3/2 = - 1.5 m/s
the wave progresses into the -x direction with 1.5 m/s
see 3d picture of progressing wave:
http://www.wolframalpha.com/input/?i=u%2…
3)?
OG