A wire with mass 40.0 g is stretched so that its ends are tied down at points 80.0 cm apart. The wire vibrates in its fundamental mode with frequency 60.0 Hz and with an amplitude at the antinodes of 0.300 cm. (a) What is the speed of propagation of transverse waves in the wire?

Video transcript

Hey everyone, welcome back in this problem. We have a physics student. Ok. And they have a one m string and it's fixed at both ends. Okay. And they're gonna pluck that string if this string fixed at both ends. Ok? You can imagine it doing kind of this when it oscillates this or this and we know that the string is one m. Okay, so this distance is length between these two ends. It's going to be one m. All right, So there's our length. one m. All right. We're told the fundamental frequency and amplitude are measured using a high speed camera. Okay, um the fundamental frequency. Okay, so F Is 80 Hz, 80 Hz. Mhm. We know that the unit of Hertz is just going to be 80 inverse seconds. Okay. And we're told that the amplitude and an anti notice six centimeters. Okay, so an anti note where we have the highest amplitude. So, here, And if we imagine that's so the amplitude here is going to be 6cm. Alright. And what we're asked to find is we're asked to find the speed of the wave and the strength. Now, let's recall. How do we find the speed of a wave but we can find the speed of a wave the by taking lambda times the frequency F. Okay, so, we know f We've been given F in the problem, We don't know lambda and lambda recall is your wavelength. Okay, so what is the length of that wave? Well, let's look at our diagram here. Okay, we know that we have this one m distance here and we can actually see that this is going to be half of the wavelength. Okay, so this distance here, we're going to be lambda over to. Okay, so we're not going from the starting point back to the starting point, we're going from the starting point kind of halfway. So we're gonna have a lambda over two. So what this tells us is that lambda over two is going to be equal to one m distance? Well, this tells us that λ is equal to two m. So now we have our lambda, we have our frequency F and we can go ahead and find our speed. So our speed is going to be lambda two m K times frequency, which is 80 hertz, or in this case we're going to use 80 Inverse seconds case of course. And this is going to give us a value of m/s. Okay, so that is the speed of the wave in the string. That's going to be answer. C. That's it for this one. Thanks everyone for watching. See you in the next video