You measure the intensity from a sound source to be 0.3 W/m 2 at a distance of 3.4 m. What will the intensity be if you walk closer to the source, to a distance of 2.5 m?

Hey, everyone. Welcome back. So in this problem, we have a sound source that's emitting in all directions, and we're told the intensity at a certain distance. So we're gonna use that to figure out what the intensity is at a closer distance of 2.5 meters. What's the intensity going to be if you move closer to the sound source? Let's go ahead and get started here. Basically, if I sort of draw a little diagram like this, imagine I have a sound source that sort of radiates in all directions. Right? So at a certain distance of 3.4 meters, what I measured there is that the intensity is equal to 0.3. So what I'm gonna do is I'm gonna call this r one. R one is a 3.4, which makes this I one. So now what happens is I wanna figure out what happens if I move closer to the source. So now let's let's see what happens if I move a little bit closer this way, such that my distance now, r 2 is equal to 2.5 meters. So what happens is I'm getting closer to the sound source, so theoretically, the sound source or the intensity should go higher. Right? I'm getting closer to the source, so I should have a higher intensity. That's basically what I'm sort of, you know, anticipating here. So let's go ahead and set up the problem. This is really kind of just like an inverse square law because we're gonna be comparing intensities at 2 different distances. Now if you remember what happens here, if I'm trying to find I 2, what I'm gonna do is say I'm gonna set up the equation. The equation for this is that I one divided by I two is equal to remember, you have to flip the numbers now. So I one over I two is r two squared over r one squared. Alright. Really, what we have is we have 3 out of 4 variables. I have I 1, I have r 2, and r 1, so I can figure out what this I 2 is going to be. Right? So pretty straightforward. So basically, what's gonna happen here is I can sort of flip the equations, and this is gonna be so I'm gonna say that this is gonna be I 2 over I 1. So, basically, just flipping it, but then I have to flip the other side as well. So this is gonna be r 1 squared over r 2 squared. It just makes it a little bit easier because now all I have to do to get this I two by itself is move this I one to the other side. So really what happens is that I 2 is just going to be this is gonna be I 1 parenthesis, and this is gonna be r 1 squared over r 2 squared. Alright? So now what I can do is just go and plug it on my numbers. What's I one? I one is just the 0.3. That's the 0.3. And then which number which number is the r one squared? Well, that's the distance that was associated with the initial intensity, so that's gonna be my 3.4. So that's 3.4 squared. What's the new distance, r 2? That's just gonna be 2.5. So I'm gonna do 2.5 squared. Now if you just go ahead and plug in all these numbers in, that's really all you need to calculate the intensity, and what you should see is either the intensity should become 0.55. And, again, that's in gonna be in watts per meters squared. Alright? So as expected, what happens is that you get closer to the source, and the intensity goes up. We were initially at 0.3 and sorry. We were initially at 3.4, and the intensity was 0.3. Now we're a little bit closer to 0.5, and the intensity grows to 0.55 watts per meter squared. So the answer choice is c. That's it. That's it for this one. Thanks for watching. Let me know if you have any questions.

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You measure the intensity from a sound source to be 0.3 W/m2 at a distance of 3.4 m. What will the intensity be if you walk closer to the source, to a distance of 2.5 m?

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You measure the intensity from a sound source to be 0.3 W/m² at a distance of 3.4 m. What will the intensity be if you walk closer to the source, to a distance of 2.5 m?