### Video Transcript

A wave is modeled by the
wavefunction π¦ as a function of π₯ and π‘ is equal to 0.30 meters times the sin of
two π over 4.50 times the quantity π₯ minus 18.00π‘, where π₯ is measured in meters
and π‘ is measured in seconds. Find the amplitude of the wave. Find the wavelength of the
wave. Find the speed of propagation of
the wave. Find the frequency of the wave. Find the period of the wave.

We can label our wave amplitude
capital π΄, the wavelength π, the wave speed π£, the wave frequency π, and the
period capital π. We can start solving for these
various wave properties by recalling that a one-dimensional transverse wave is
modeled by the function π¦ is a function of π₯ and π‘ is equal to wave amplitude
times the sine of wavenumber π times position minus angular frequency of the wave
times time.

Looking back at our given wave
function, we see right away that the amplitude of our wave is given as 0.30
meters. To solve next for the wavelength of
our wave π, we can recall that wavelength and wavenumber are related. Wavenumber π is equal to two π
over wavelength. And as we look at our given
function, we see that this is two π over 4.50. This indicates that our wavelength
π is 4.50 meters.

Next, we want to solve for wave
speed π£. And to do this, weβll recall two
pieces of information. First, we recall that angular
frequency is equal to two π times frequency π. Working off of our given wave
function, we see that two π times 18.00 divided by 4.50 is equal to π, which is
two π times π. The factors of two π cancel
out. And π is equal to 4.00 hertz. We can fill that in for our
frequency π in advance. But now we wanna use the
relationship that says π£ is equal to π times π to solve for π£. π£ is equal to ππ or 4.50 meters
times 4.00 hertz, which is equal to 18.00 meters per second. Thatβs the speed of propagation of
this wave.

Finally, we want to solve for the
wave period π. Recalling that wave period is equal
to the inverse of wave frequency, the period of this wave is equal to one over 4.00
hertz or 0.250 seconds. Thatβs the wave period determined
using the wave function for a wave as well as relationships among wave
parameters.