Please show me step by step solution and explanation for this.Sorry if this is too much but I really need help
A progressive wave 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 "progressive wave" 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 position of this wave's peak on the x-axis?
A progressive wave 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 "progressive wave" 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 position of this wave's peak on the x-axis?
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1/ (..)^4 , what a strange function
a wave equation is one in which the displacement is a function of time and place
a picture of it with respect to place is frozen in time t constant so v = df/dx
if you freeze place, so x is constant it varies with t
common waves are f( sin x/ X + sin t/ T) where X and T are constants
notice a sin function needs a pure number that has NO unit that is why the x/X value has its position units "cancel out"
determining the wave function based on experiments or theories of the derivitives of the funtion is VERY difficult math
a wave equation is one in which the displacement is a function of time and place
a picture of it with respect to place is frozen in time t constant so v = df/dx
if you freeze place, so x is constant it varies with t
common waves are f( sin x/ X + sin t/ T) where X and T are constants
notice a sin function needs a pure number that has NO unit that is why the x/X value has its position units "cancel out"
determining the wave function based on experiments or theories of the derivitives of the funtion is VERY difficult math