Relevant concepts:

$-$ wave function for a sinusoidal wave:

y$($x$,$t$)=$ A sin $($kx $$t $+)$

$-$ speed of a sinusoidal wave: v $=/$k $=$f

$-$ angular wave number: k $=2/$

$-$ angular frequency: $=2/$T $=2$f

$-$ transverse speed of an element of a wave on a string: $$y $=$y$/$t

$-$ transverse acceleration of an element of a wave on a string: $$y $=$y$/$t

The wave function for a traveling wave on a taut string is $($in SI units$)$

y$($x$,$t$)=0\mathrm{.}360$ sin$$

$6$t $2$x $+$

$35$

To begin, express the given wave equation

y$($x$,$t$)=0\mathrm{.}360$ sin $(6$t $2$x $+3/5)$

in the general form of the wave function equation:

y $=$ A sin $($kx $$t $+)$

using the trig identity sin$()=$ sin$(+).($This will take a little work!$)$ Once you have it expressed in the general form, you can determine the values of the constants k$,,$ and $.$

What are the values of the following constants $($enter your answers as factors of $)$:

angular wave number: k $=$

angular frequency: $=$

phase constant: $=$

$($a$)$ What are the speed and direction of travel of the wave?

speed m$/$sdirection$---$Select$---$positive x$-$direction$$positive y$-$direction$$positive z$-$direction$$negative x$-$direction$$negative y$-$direction$$negative z$-$direction

$($b$)$ What is the vertical position of an element of the string at t $=0,$ x $=0\mathrm{.}180$ m$?$

m

$($c$)$ What is the wavelength of the wave?

m

$($d$)$ What is the frequency of the wave?

Hz

$($e$)$ What is the maximum transverse speed of an element of the string?

m$/$s