A string that is under 50.0 N of tension has linear density 5.0 g/m. A sinusoidal wave with amplitude 3.0 cm and wavelength 2.0 m travels along the string. What is the maximum speed of a particle on the string?

Video transcript

Welcome back, everyone. We are making observations about the following wire. Here we are told the wire is strained to a tension of 145 newtons. We are told that its linear mass density is 0.8 kg per meter. Now a sine wave is sent on the wire and we are told that the sine wave has an amplitude of 4.5 centimeters, 4.45 m. And we are also told that it has a wavelength of 1.3 m and we need to find the greatest speed of a mass element on our wire. Well, we have a formula for this. We actually have that the speed or the maximum speed for us of a mass element on the wire is simply equal to our angular velocity times our amplitude. We know that angular velocity is equal to two pi times our frequency. And we also know that frequency is equal to velocity divided by our wavelength. So I'm going to sub in and let me change colors here real quick. I'm going to sub in our equation for frequency into our equation for angular velocity. What we get is that angular velocity is equal to two pi times our wave speed divided by our wave length. Now finally, I will sub in our equation for angular velocity into our equation for our speed of a mass element. And what we get is we get that the speed of a mass element is equal to two pi times our amplitude times our wave speed divided by our wave length. But what is our wave speed here? Well, wave speed is going to be found by taking the square root of the tension divided by our linear mass density. So let's go ahead and calculate that. What we get is we get the square root of 1 45 divided by 0.8. And this gives us 134.6 m per second. So now we are ready to find our speed of a mass element here. What we have is that we have B Y max is equal to two pi times 20.45 times 34.6 all divided by 1.3. And when we plug this into a calculator, we get a final answer of 29.3 m per second, which corresponds to our final answer. Choice of a. Thank you all so much for watching. Hope this for your help. We will see you all in the next one.