FIGURE EX17.7 shows a standing wave on a string that is oscillating at 100 Hz. a. How many antinodes will there be if the frequency is increased to 200 Hz?

Video transcript

Hello, fellow physicists today, we're gonna solve the following practice problem together. So first off, let's read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Anti nodes are points of maximum displacement in standing waves in the figure below a standing wave on a string oscillates at a frequency of 200 Hertz. If the frequency were to be doubled to 400 Hertz keeping the wave speed constant, how many anti nodes would be present in the resulting wave pattern? So that's our end goal is to determine how many anti nodes would be present in the resulting wave pattern. So we're given some multiple choice answers. Let's read them off to see what our final answer might be. A is three, B is six C is nine and D is 12. So first off recall that the velocity of a wave is V is equal to the velocity is equal to frequency multiplied by the wavelength. We can also then go on to write that wavelength prime multiplied by frequency prime is also equal to the velocity of a weight. So note that when the frequency is doubled to 400 hertz from 200 Hertz. We can write that frequency prime is equal to two times the frequency. So the wavelength will also be reduced to half its value. So we can write that the wavelength multiplied by the frequency is equal to wavelength prime multiplied by two times the frequency, which we can also write that wavelength prime is equal to wavelength divided by two, which this is shown in our diagram given to us by the problem itself. So to help us visualize this problem, let us draw a couple of sketches here. So let's draw a little oscillating wave here. The string, the standing wave, let's draw it. We have 12, three, so 123 separate our nodes here. So from the start of the wave to this point would represent the wavelength as shown in our diagram. And from here to hear would be wavelength divided by two. But so this is shown in our again, like I drew it again. But the emphasized. So now we need to consider what will happen when it's doubled. So carry down or little nudes here, we have to, there's gonna be the one node here that we had originally. Once it's double, there's gonna be two nodes instead. So this would be wavelength prime. So therefore the number and nodes try to get everything to fit on one screen. Therefore, the number of anti nodes will increase from 3 to 6. So that means looking at our multiple choice answers, the correct answer has to be the letter B six. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.