00:01
This question asks us about a trombone with a frequency of 280 hertz.
00:07
I believe, and i don't really understand trombones all that well, but i believe that what we're talking about here is that this distance is 80 centimeters, 0 .80 meters.
00:21
And so this curved part here is 0 .10.
00:27
No, they wouldn't be 0 .10.
00:34
They're saying that the distance here is 0 .10, and this is a circle.
00:41
So, a semicircle.
00:45
That means the radius would be 0 .05 meters, the radius of that circle.
00:54
The circumference, or at least half the circumference, would there be pi times 0 .05.
01:04
Meters.
01:06
And so the total length is going to be 0 .80 plus 0 .80 because there's two of them, plus that semicircle, the circumference of that semicircle, half circumference, which would be 0 .05l.
01:39
S.
01:40
So i'm going to put that in there too.
01:42
If you extend the slide, that's going to put two s onto it because there'll be an s here and there'll be an s here.
01:52
All right.
01:59
Now, frequency is v over to l.
02:11
And so, wait a minute, let me back up a little bit.
02:28
I'm going to take that back.
02:30
I'm not sure i fully understood the question.
02:33
I don't think we have the whole trombone here.
02:36
We just have the slide.
02:38
So we've got a microphone, not a microphone, but a sound wave, like a tuning fork, here.
02:54
And it's transmitted through the tube.
03:03
And so it's detected here.
03:11
So detect here.
03:14
And i'm going to call this fork here, the tuning fork.
03:17
All right.
03:18
So the change in the length is going to be the full length, which i have written there in red, minus the distance between the fork and the detector, which would be 0 .1.
03:40
So that's going to give me, and now i'm wondering, where did this l come from up here? add those two plus half .0 .05.
04:08
That's supposed to be pi.
04:15
There we go.
04:16
0 .05 pi.
04:17
Half the circumference was 0 .05 pi.
04:20
And then 2s.
04:24
Okay.
04:27
Add these together and i get 1 .6.
04:32
If i subtract d, d is 0 .1.
04:36
So that's going to give me 1 .5.
04:40
So one, you know what, i'm just going to write the whole thing.
04:54
Minus .1.
04:56
Because that's the distance between the fork and the detector.
05:00
1 .5 plus 0 .05 pi plus 2 .s.
05:08
So that's going to give us delta l.
05:16
Now, constructive interference is going to occur when delta, x, which is the same as delta l in this case, is lambda m, some multiple of lambda.
05:31
So, m is delta l over lambda.
05:49
Speed is wavelength times frequency...