The string in FIGURE P16.59 has linear density μ. Find an expression in terms of M, μ, and θ for the speed of waves on the string.

Video transcript

Welcome back, everyone. We are making observations about the following system right here where we have a mass that we are told as a mass of three kg, we have a mass per unit length on this wire holding up the mass of 0.35 kg per meter. And we are tasked with finding how fast the waves travel along the wire. Well, what we are going to do as you can see, we've redefined our coordinate system to where we have our X axis parallel to the inclined here. What we're gonna do is we're going to apply Newton's second law along the X direction here. Now, we know that this system is stationary. So the right hand side of our equation is simply going to be zero. But what about the left side? What is the net force uh in the X direction here? Well, this is going to be the tension of the wire minus the X component of the weight of our block. So that'll be M G times sign of our angle theta we have. However, that the formula for our velocity of the waves is going to be the square root of our tension divided by our mass per unit length. So let's go ahead and plug in our values we have that the velocity is equal to the square root of M G sine of theta sense E minus M G S sign of theta equals zero. Therefore, T is equal to M G S sign of the divided by our mass per unit length. So let's go ahead and plug in our values. What we get is we get that the velocity is the square root of three times 9.8 times the sign of our angle which is 30 degrees divided by 0.35, which when you plug into our calculator gives us a final answer of 20.5 m per second corresponding to our answer. Choice of a. Thank you all so much for watching. I hope this video helped. We will see you all in the next one.