#wave phenomena

31/07/2020 19:13

This week has been a Mess with a capital M but I thought I’d finish July’s questions for @myhoneststudyblr‘s challenge then do sat/sun in a couple days then do it weekly after that (tho I might do it more regular but I don’t know y’all we’ll see)

|M| 27th July: Do you stay indoors or outdoors more in the summer?

I think I tend to do both. When we’re at home, I’d usually go with my parents for mundane things like groceries just to go outside.

|T| 28th July: How do you stay motivated to study during the summer?

If I’m studying during summer, it means I’ve got something important coming up, so I keep myself motivated by reminding myself what I’m doing it for. I also don’t study a lot in one day? I’ll do like... 3 hours, max because I don’t see a point in doing more than that. 

|W| 29th July: Have you done or are you planning to do any activities (such as work experience, summer schools or watching lectures) other than normal work during the summer?

I was going to do volunteer work at the rabbit shelter I was with last year, but covid’s put a halt to that plan :( 

|T| 30th July: Beach or Swimming pool?

Swimming pool

|F| 31st July: What do you like most about the beach?

I like how open it feels, and the sand’s fun enough in the moment. 

There are two ways you can think about this conceptually:

1. Suppose you have a generic wave described by the equation y = sin(kx + wt). After a given time from the start of its journey, t has increased. The golden rule is that the entire term inside the sin or cos function remains constant. So when t has increased, the value of (kx + wt) has increased. To compensate, x will decrease by an amount to compensate for the increase in t. And, of course, a decrease in x means that its displacement is in the negative direction.

The converse is true. So when you  have y = sin(kx - wt), after a certain time t has increased, and so the value of (kx - wt) has decreased. To compensate, x will increase, hence the motion in the positive direction.

The next most likely question is “Why does the term inside the sinusoidal function have to remain constant?” If you’re thinking about part of a part of the wave moving, then after a certain time t, you want to find that same part of the wave again to see where its moved to, which is why you’re looking for the same y-value. And if you’re looking for the same y-value, then you’re looking to keep the term inside the function constant.

2. What helps me remember it better is thinking about transformations of graphs, mathematically. If you had f(x) and f(x + k), the latter is the former shifted to the left, or the negative x-direction. This is because when a constant is added inside the function, the term is increased, and so the corresponding y-value occurs ‘sooner’ for a given x value, hence moving to the left. I’m not sure to what extent this is technically applicable to this situation in physics, but it fits, and if it helps remember the direction of propagation then why not?

Wonderful video submission from occultus-vita

Gives You Sound: a song about wave phenomena