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 (b) wavelength.

Accepted Answer

Hey everyone welcome back in this problem. We have to sinus idol waves. Okay? They're traveling in opposite directions along a string and they interfere and they produce a standing wave and the standing wave can be described by the equation Y. X. Of T. Is equal to three sine pi of X. Sign 50 pi of T. Okay, we're given the units. And what we want to find is what is the wavelength of the two traveling waves? Alright, so let's first recall. We're talking about wavelength when we have interfering waves, the wavelength of the standing wave is going to be the same as the wavelength of the traveling waves. Okay. And so what we want to find is we can find the wavelength of the standing wave. Okay, so let's write the general form for the standing wave equation. Okay, so we have Y. X. Of T. Is equal to two A sine of K. X. Sine of omega T. Alright, so we want to find the wavelength which we know is lambda. How can we relate that to this equation? Well let's recall the K. The wave number in this equation. Okay, here Can be written as two pi over lambda. Okay and so here we're looking for lambda and this is our direct relation to lambda from this equation. Ok, so let's try to figure out the K value from our equation. That'll let us find lambda. So looking at the equation we're given and comparing it to the general form, we see that K is going to be pie. Okay, so we have pie on the left hand side is equal to two pi over lambda. Okay, multiplying lambda to the left hand side and dividing by pi is going to give us lambda is equal to two centimeters. Okay, so that's the wavelength we were looking for. That's the wavelength of the standing wave, which is equal to the wavelength of those traveling waves. And so the answer is going to be a thanks everyone for watching. 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 (b) wavelength.

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