The wave function of a standing wave is y(x, t) = 4.44 mm sin[(32...

Question

The wave function of a standing wave is y(x, t) = 4.44 mm sin[(32.5 rad/m)x] sin[(754 rad/s)t]. For the two traveling waves that make up this standing wave, find the (a) amplitude.

Accepted Answer

Hey everyone, welcome back in this problem. We have a nylon guitar string and it's vibrating. According to the equation Y equals 0.2 sine of 2. X. Sine of 40 pi T. Okay, when we're asked to find the amplitude of the two transverse cell waves from the standing wave. Okay, now let's recall the general form of the standing wave equation. We know it's going to be y is equal to to a sign of K X. Sign omega T. Now in this case A is the amplitude of those transverse waves. Okay, so A is actually what we're trying to find. Okay, so comparing this to the equation we're given, we can write that to a Okay here, this to a term in front. Well that's going to be 0.2. Okay, so we have to a is equal to 0.2 dividing by two. We get A. Is equal to 0.1 in our unit. Is centimeters. All right. So the amplitude of those to transfer cell waves is 0.1 centimeters. That's going to be answer A. That's it for this one. See you in the next video

The wave function of a standing wave is y(x, t) = 4.44 mm sin[(32.5 rad/m)x] sin[(754 rad/s)t]. For the two traveling waves that make up this standing wave, find the (a) amplitude.

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