You may have had an opportunity to skip rope or watch someone else skip rope. If...

You may have had an opportunity to skip rope or watch someone else skip rope. If you have one rope, you can skip by yourself or you can include two friends, each friend holding one end of the rope with you skipping in the middle. In this instance, your friends represent nodes, and you an antinode.

a) Is it possible to skip rope with three friends with two of you in the middle jumping at different time?

b) How can two jumpers be in the middle in a way that only one person has to jump at a time? Could you, if you can, refer to terms node, antinode, and frequency as you answer this question?

Thank you so much!!

Solutions

Expert Solution

Case 1:

Let us first take the situation when I skip the rope whereas my two friends holding the string together at both ends.

So technically, the two ends are the 'nodes' of the wave that is created by them(friends). The situation can be depicted as follows. Consider, a string vibrating between two fixed rigid walls (in this case the friends). They produce the vibration of the string with the fundamental frequency (see attached figure 1 for references) while the wall serving as node position.

Case 2:

Now Coming to the 2nd part where think that, somehow my friends produce the first overtone frequency for the vibration of the string.

Where still the two nodes are in the end as in the previous case. In addition to that, there is an extra node at the middle of the vibrating string that we will jump over. This is the same case as for a string between two rigid walls with the first overtone. Now if you carefully look at the attached figure 2, you can clearly see that the vibration is divided into the two regions with opposite phase with a node at the middle and two nodes at both ends. If I start jumping over the left half of the vibration at a certain time, my friends will not be able to start jumping at that time instantaneously. But after when I will have completed my one jump, He/she should immediately jump over it else we cannot continue skipping. So eventually one of us will be jumping at a time but not simultaneously.

Now the question comes to mind how can we produce such a scenario of vibration?

Well, there is a brute force way. If we fix the middle of the rope to ground artificially then this kind of wave can be produced.

Else, two of the people holding the rope will have to vibrate the rope without of phase to each other to create a standing wave like this.

genius_generous answered 1 year ago

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