We also denote another important parameter for waves: the amplitude $A,$ which is half the distance between peaks and troughs $($the minimum points of the wave$),$ respectively.

In addition to the period, another important parameter we use to describe waves is the wavelength, $.$ This can be visualized by taking a snapshot of our wave at some time, say $t=0,$ and plotting the vertical displacement of the wave as a function of position as shown below on the left in figure $($b$).$ Just as with the period, if we pick any point on the wave, the wavelength is the distance between that point and the next point on the wave with the same $y-$value and the same slope.

$($b$)$

$($c$)$

The second figure above, figure $($c$),$ shows this wave both at $t=0$ and at some short time $t>0$ later, where it appears to have moved to the right, but a point $($denoted by the star$)$ on the string actually moves down: The points on the string only moves vertically, not to the right as the wave itself travels. We think of the wave propagating to the right $($in this case$)$ because that is the direction energy is transferred by the wave.

We denote the wave velocity as $v,$ which depends on the material that is being disturbed by the wave motion. For a string, one can show the wave velocity involves only the force of tension $F_T$ holding the string taut and the mass per unit length, or linear mass density $($which has SI units of $k\frac{g}{m}).$ Additionally, the velocity can be determined if we know the wavelength and period.

Consider the point of the wave denoted by the circle in figures $($a$)$ and $($b$)$ above. This point appears to move to the right, which correctly describes the motion of the wave. What would the average velocity $v$ of that point be in terms of $$ and $T?$ Given that the frequency of the wave is $f=\frac{1}{T},$ what is the wave velocity in terms of the wavelength and frequency?