Find the Amplitude Equation

Question

A wave has the following equation:

y=0.3(0.7+1.2cos(pi/2))

What is it's Amplitude?

Is it just 0.3 because that's what I thought?

Answer 1

A standard form for a periodic wave is S = A*sin(ωt), where A is the "half-amplitude" (i.e. 0 to peak), and ω is the angular frequency in radians / second.

Let's apply this definition to your problem:

y=0.3(0.7+1.2cos(pi/2))

First there is no independent variable, so let's fix that:

y=0.3(0.7+1.2cos(t*pi/2))**

Next, expand the right hand expression:

y=0.21 + 0.48cos(t*pi/2))

This describes a sinusoid with a fixed amplitude offset of 0.21 and an amplitude of 0.36

**OR--it might be something like cos(ωt + pi/2)

(not relevant to your question, but: to put that into standard form, one would write a sin function and then put in an angular offset to make it equivalent

Answer 2

I suspect there's an x missing somewhere in your problem statement because as written it isn't a wave (it's just a number). Assuming there's an x somewhere within the cosine argument, the amplitude is the factor in front of the cosine. Distribute the 0.3:

y = 0.3(0.7 + 1.2 cos(pi/2))

y = 0.21 + 0.36 cos(pi/2)

The amplitude is the factor in front of the cosine = 0.36.