Question

A particular sound wave can be graphed using the function y=1 sin 4x. Find the amplitude and period of the function.

Answer 1

We know that sin(x) attains values between -1 and 1, so the amplitude is the highest distance above the x-axis it goes (i.e., the number multiplying the sin(x) term). In this case, the amplitude would be 1.

The period, on the other hand, can be calculated as followed: if T is the period, and f is the frequency, then the period of the function sin(fx) is\[T = \frac{2 \pi}{f}\] You can see this by looking at what the frequency is: it tells you how many times the oscillation happens in one range of angles spanning 2π. Then, dividing 2π by the frequency will tell you how long each oscillation takes. In this case, it's 2π/4 = π/2.