For the wave described by $y=0.15 \sin \left[\frac{\pi}{16}(2 x-64 t)\right] \text { (SI units) }$ , determine the first positive x coordinate where y is a maximum when t = 0.
A)16 m
B)8 m
C)4 m
D)2 m
E)13 m

Question

Quizplus · Accepted Answer

The equation provided is a cosine wave with amplitude 2 and period $2\pi/4=\pi/2$. The maximum value of the cosine function is 1, so the maximum value of the wave function is 2. We want to find the first positive x coordinate where this maximum occurs, which is when $y=2$ and $t=0$. Substituting these values into the equation, we get:

$2 = 2\cos(\frac{\pi}{2}x)$

Simplifying and solving for $x$, we get:

$x = \frac{2}{\pi}\cos^{-1}(1) = \frac{2}{\pi}(0) = 0$

However, we want the first positive value of $x$, so we need to find the first positive value of $x$ where the cosine function is 1. This occurs at $x = \frac{\pi}{2}$, so the answer is:

Answer: C (4 m)

For the Wave Described By y=0.15sin⁡[π16(2x−64t)] (SI units) y=0.15 \sin \left[\frac{\pi}{16}(2 x-64 t)\right] \text { (SI units) }y=0.15sin[16π​(2x−64t)] (SI units)

For the Wave Described By $y=0.15 \sin \left[\frac{\pi}{16}(2 x-64 t)\right] \text { (SI units) }$