[amp_mcq option1=”Both will reach their minimum values at the same instant” option2=”Both will reach their maximum values at the same instant” option3=”When one wave reaches its maxi¬mum value, the other will reach its minimum value” option4=”None of the above” correct=”option3″]
The correct answer is: C. When one wave reaches its maximum value, the other will reach its minimum value.
A sine wave is a periodic function of time that repeats its values over and over again. The frequency of a sine wave is the number of times it repeats its values in one second. The phase of a sine wave is the position of the wave relative to its starting point.
Two sine waves of the same frequency have a phase difference of $\pi$ radians if they are out of phase by one-half cycle. This means that when one wave reaches its maximum value, the other wave will reach its minimum value.
Here is a diagram of two sine waves with a phase difference of $\pi$ radians:
[asy]
unitsize(1 cm);
draw((0,-1.2)–(0,1.2));
draw((0,0)–(4*pi,0));
real g(real t) {
return sin(t);
}
real h(real t) {
return -sin(t + pi);
}
draw(graph(g,0,4pi),red);
draw(graph(h,0,4pi),blue);
label(“$y = g(t)$”, (2pi,1), E);
label(“$y = h(t)$”, (2pi,-1), E);
[/asy]
As you can see, the two waves are out of phase by one-half cycle. When one wave reaches its maximum value, the other wave reaches its minimum value.