A sound source radiates sound waves in all directions. At a distance of 4 m from the source, you measure the wave intensity to be 0.06 W/m 2 . How much sound energy does the source emit in 1 hour if the power output is constant?

Everyone, welcome back. So in this problem, we're told that a sound source like a speaker or a siren or something like that is gonna radiate sound waves in all directions, and we're told that at a distance of 4 meters from the source, the intensity is 0.06. What we wanna figure out is how much sound energy gets produced in 1 hour if the power output is constant. So there's lots of stuff going on here in this problem. There's distances, there's intensities, energies, and powers. We'll definitely be able to use our equations for wave intensity to solve this. So let's get started here. So first of all, notice how they're giving us a distance. And in these kinds of problems with wave intensity, that's always gonna be r. So we're told that r is equal to 4. The intensity of that sound source at a distance of 4 meters is 0.06. Now what we're really trying to find here is some kind of an energy. That's the variable e. So what is that? So how do I figure what e is? Well, really, the way that energy and power are related is just by the p equals e over delta t equation. So, really, from p equals e over delta t, that's just energy power equals the definition of power, which is energy over time, we can rearrange this equation and say that energy is equal to power times delta t. So p times delta t. Alright? In order to figure out the amount of energy, then I have to figure out the amount of power, and then I just multiply it by some time. What's the time? Well, it's really just the delta t that they're giving us, the 1 hour. So, really, what happens is I'm just gonna scoot this down for a little bit, and so I'm gonna say that my delta t is 1 hour. And if you convert this, because hour is not an SI unit, this actually ends up being 60 times 60, which is gonna be 36 100 seconds. So that's how many seconds are in an hour, and that is an SI unit here. So, basically, what happens here is if I can figure out the power output of the source and just multiply it by my time, which is 36100, then that's gonna be the total amount of energy that's produced by the sound source here. So really, this is what I'm trying to find. Now how do I find the power? Well, I just relate it to my wave intensity equation. So how do I find p? Well, really what happens is I'm just gonna bring this over here. My p average is just gonna equal as it just related to my intensity equation. Right? So p average. So what I'm gonna do is I'm gonna say the intensity is equal to my average power output divided by 4 pi r squared because it's a spherically it's gonna radiate in all directions, so that's just gonna be the surface area of a sphere or something like that. Alright? So let me rearrange this equation a little bit, and basically that my power average is just going to be is just going to be the intensity times 4 pi r squared. Alright. So in other words, my power is just going to be the intensity, which is 0.06 times this is gonna be 4 pi times 4 squared. Alright? Now if you work all of this out, what you're gonna get here is you're gonna get an intensity of 12 I'm sorry, a power output of 12.06, and that's in watts. So that's gonna be the SI unit. It's 12.6 joules per second. That's a watt. So now I just take this number over here that I got for power, and I'm gonna plug it back into this equation. Alright? So that just really goes back into here. Alright? So my total energy output for the hour for the sound source or the speaker or siren or something like that is just gonna be 12 0.06 watts that I got from the wave intensity equation, and I just multiply it by 33,600 seconds. And what you get when you work this out is you should get a total power or sorry, energy output of 43,400 joules. So that is the final answer. Alright? So if you look through your answer choices, you'll see that this is gonna be answer choice d. Alright? Thanks for watching. Let me know if you have any questions.

Physics with Algebra 때문에 힘들어하고 계신가요?

A sound source radiates sound waves in all directions. At a distance of 4 m from the source, you measure the wave intensity to be 0.06 W/m2. How much sound energy does the source emit in 1 hour if the power output is constant?

다음 시청

A sound source radiates sound waves in all directions. At a distance of 4 m from the source, you measure the wave intensity to be 0.06 W/m². How much sound energy does the source emit in 1 hour if the power output is constant?