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Riding the Sine Wave…

December8

A sine wave is a repetitive change or motion which, when plotted as a graph, has the same shape as the sine function.spring

For example, on the right is a weight suspended by a spring. As it bounces up and down, its motion, when graphed over time, is a sine wave. In reality, friction and air resistance would cause the bouncing to slow down and eventually stop, but for illustration purposes we ignore that here.

Sound waves are very quick changes in air pressure which your ear interprets as sounds. For very pure single tones, a plot of air pressure against time would show them to be sine waves. For audio tones like this, pressure is cycling hundreds or thousands of times per second.
amplitudeThe height of a sine (or other) wave is called the “amplitude”. Another way to think of this is that it represents how much the sound increases (or decreases) in volume.
When you are at the beach you will notice that the waves come in almost regular intervals. The gap between the tops of the waves is called the “period” and this is the same if you take the distance between any two identical points on the wave: period

In Mathematics, we study functions like the Sine curve, as it opens up so many practical applications to engineering and science, as well as music and hydrology and …. – you get the picture?

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y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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