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physics question

aarond280

http://examinations.ie/archive/markingschemes/2011/LC021ALP000EV.pdf
Why in question 8(b) is area 4pi(8)^2, where did the 4 come from ?

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Chavways

aarond280 wrote: »

http://examinations.ie/archive/markingschemes/2011/LC021ALP000EV.pdf
Why in question 8(b) is area 4pi(8)^2, where did the 4 come from ?

The formula 4piR^2 relates to the area of a sphere. I cant see if its even mentioned in the question that the speaker is a sphere but that's why they use that formula.

decisions

It's not that the speaker is a sphere, it's that the sound waves emitted from a speaker will always be in the shape of a sphere or a hemisphere if it is mounted on a wall.

jamo2oo9

Would it not be in cone shape?

Leaving Cert Student

jamo2oo9 wrote: »

Would it not be in cone shape?

No I think that's for light!

Brendan1234

Leaving Cert Student wrote: »

No I think that's for light!

As far as I know light also travels out in the shape of a sphere i.e. it travels out in all directions

When you think about it it makes sense that sound travels in all directions, otherwise you wouldn't be able to hear what somebody says unless they were facing you.

Leaving Cert Student

Brendan1234 wrote: »

As far as I know light also travels out in the shape of a sphere i.e. it travels out in all directions

When you think about it it makes sense that sound travels in all directions, otherwise you wouldn't be able to hear what somebody says unless they were facing you.

Yeah but light has a much shorter wavelength and diffracts much less than sound. Unless I am mistaken, light would make sense to travel out in the shape of a cone

Chikablam

Leaving Cert Student wrote: »

Yeah but light has a much shorter wavelength and diffracts much less than sound. Unless I am mistaken, light would make sense to travel out in the shape of a cone

Well yes, it would.......when it's refracted.
But under normal circumstances, it'd just travel in all directions, or a sphere

Leaving Cert Student

Chikablam wrote: »

Well yes, it would.......when it's refracted.
But under normal circumstances, it'd just travel in all directions, or a sphere

For DCG, we learn that a flashlight emits light in the shape of a cone.
This is because light travels in straight lines (not 100% true, but close enough).
Conversely sound expands in all directions as it is a wave. I am not completely sure but I am struggling to think light would be calculated using a sphere...

Brendan1234

Leaving Cert Student wrote: »

Yeah but light has a much shorter wavelength and diffracts much less than sound. Unless I am mistaken, light would make sense to travel out in the shape of a cone

I might be reading into this incorrectly, but are you saying the reason sound spreads out in all direction when people speak is because of diffraction?
I'm pretty sure this isn't the case because the frequency with which you speak changes, and so does the wavelength so then your voice would only diffract some of the time around your mouth. As a ballpark figure though the wavelength of sound produced by a person would be in or around a metre (quite a large range though), so it couldn't be because of diffraction because your mouth is too small.

For DCG, we learn that a flashlight emits light in the shape of a cone.
This is because light travels in straight lines (not 100% true, but close enough).
Conversely sound expands in all directions as it is a wave. I am not completely sure but I am struggling to think light would be calculated using a sphere...

I could be wrong, but i think the reason light emits in the shape of a cone in the case of a flashlight is because it is essentially "funnelled" by the plastic cover. If you look at light bulbs attached to your ceiling, it looks as though the light is emitted in a sphere (or hemi-sphere).

Chikablam

Brendan1234 wrote: »

I might be reading into this incorrectly, but are you saying the reason sound spreads out in all direction when people speak is because of diffraction?
I'm pretty sure this isn't the case because the frequency with which you speak changes, and so does the wavelength so then your voice would only diffract some of the time around your mouth. As a ballpark figure though the wavelength of sound produced by a person would be in or around a metre (quite a large range though), so it couldn't be because of diffraction because your mouth is too small.

I could be wrong, but i think the reason light emits in the shape of a cone in the case of a flashlight is because it is essentially "funnelled" by the plastic cover. If you look at light bulbs attached to your ceiling, it looks as though the light is emitted in a sphere (or hemi-sphere).

That's exactly it
The bulb in the flashlight is emitting light in a sphere, but we only see a portion of that light, the light that travels through the glass, while the rest remains "inside" the torch.
It doesn't really matter though because, as far as I'm aware, something requiring the "shape" of light is unlikely to come up(I can't really think of how it could).
However, the "shape" of a sound-front could.
If it comes up with a speaker on a wall/floor/roof/anything flat, use the hemi-sphere formula, reason being that obviously the sound is only traveling in a hemi-sphere, one half being on a wall.
If the speaker is freely suspended, use the sphere volume.
If it doesn't say which it is, use either, as was the case with OP

decisions

If it doesn't state that it is mounted on a wall, I would use the sphere. In the question they are testing do you know this fact and can you apply it in the question. If you use the hemisphere and it is not clearly stated that it is on a wall you are at risk of loosing marks.

When that came up I'd say it caught a lot of people out.

MathsTeacherD

We don't really need to worry about the 'shape' of the wavefront emitted here, or the differences between light and sound as waves, or diffraction, or anything like that: "An audio speaker at a concert emits sound uniformly in all directions..."

Now anything that acts uniformly in all directions is usually modelled as essentially a point source, with wavefronts (in this case, though in similar examples it could be field lines for the electrostatic force or the gravitational force, or electromagnetic radiation waves) spreading out from it, expanding in all directions. As these waves move the wavefronts form spheres - sound that left the point source a specific time ago has travelled a specific distance through the air around it by now, in all directions...so it's a sphere.

Now we're measuring sound intensity at a certain distance. It doesn't matter in which direction. All of the power emitted from the source is spreading out, and we're interested in when that certain amount of power (100 W) has spread out in all directions, 8m away - we think of it passing through an imaginary sphere of radius 8m. Remember, the surface area of a sphere is 4 x pi x r^2. So, how much has that power 'spread out' over that sphere? That's the sound intensity. Sound Intensity = Power/SurfaceAreaofSphere = 100/(4)(pi)(8)^2 [W/m^2]

The main thing about the model (known as an 'inverse-square' relationship) is this: the surface area of a sphere is 4 x pi x r^2. Whatever it is that is spreading out from that point source, it passes through a spherical surface which has an area that increases not just at the same rate as the distance from the point source (the radius) increases, but according to that distance squared. So, double the radius of the sphere, and you find the intensity drops not to half of what it was, but to 1/(2^2) = 1/4 of what it was.