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## Homework Statement

A travelling pulse is given by [itex]f(x,t)=A{ e }^{ \frac { 2abxt-{ a }^{ 2 }{ x }^{ 2 }-{ b }^{ 2 }{ t }^{ 2 } }{ { c }^{ 2 } } }[/itex] where [itex]A, a, b, c[/itex] are positive constants of appropriate dimentions. The speed of pulse is:

a) [itex]\frac { b }{ a } [/itex]

b) [itex]\frac { 2b }{ a } [/itex]

c) [itex]\frac { cb }{ a } [/itex]

d) [itex]\frac { b }{ 2a } [/itex]

## Homework Equations

[itex]\tilde { f } (x,t)=\tilde { A } { e }^{ i(kx-\omega t) }[/itex] and

[itex]\omega=kv[/itex]

[itex]\tilde { f }[/itex] is complex wave function.

[itex]\tilde { A }[/itex] is complex amplitude.

[itex]k[/itex] is the wave number.

[itex]\omega[/itex] is angular frequency.

[itex]v[/itex] is the velocity of pulse.

## The Attempt at a Solution

The strategy was reduce the equation into the standard wave equation and see which part corresponds with [itex]\omega[/itex] and [itex]k[/itex]. Once we find the expression for [itex]\omega[/itex] and [itex]k[/itex], its not very difficult to find the velocity using the 2nd equation.

The equation doesn't contain [itex]i[/itex]. But reducing the equation, we get something like this,

[itex]f(x,t)={ e }^{ { (i\frac { ax-bt }{ c } ) }^{ 2 } }[/itex]. The only problem is how to get rid of the square? Using logarithms wasn't helpful.