#### platham

##### New Member
How does a steradian apply to physics, and acoustics

• #### maxiogee

##### Banned
A steradian is defined as "a unit of measurement of solid angles, the angle subtended at the centre of a sphere by an area on its surface numerically equal to the square of the radius", so I presume that, in acoustice, it refers to how sound travels from its source. I suppose in physics it applies to forces moving from a central locus.

#### panjandrum

##### Lapsed Moderator
In two dimensions, there are pi radians in a circle.

In three dimensions, there are four pi steradians in a sphere.

These seem to be eccentric notions, but measuring angles in radians and solid angles in steradians makes the maths work out neatly in a bizarre and mystical way.

Oh, adding to that little bit of delight, this is the kind of maths used in relation to anything that radiates in three dimensions from a source of some kind - such as sound, light, radiation of any kind.

And finally, though it should have been first, welcome to WordReference, platham

#### DaleC

##### Senior Member
platham said:
How does a steradian apply to physics, and acoustics

That's really a science issue, not a language issue. But here's a bird's eye view. An angle is a region, a piece of space. Imagine a circle. It may occur that an object travels along the circle itself; then you would be measuring various motion quantities (acceleration, speed, velocity, momentum). It may occur that matter or energy -- sound energy, say -- passes through part of the area enclosed by the circle; then you would be measuring intensities, concentrations; namely: densities (concentration per unit space) and fluxes (concentrations relative to both space and elapsed time). Obviously, you can have motion in three dimensions as well as two.

Acoustics is about the motion and intensity of sound energy. Sound emanating from a point radiates -- and dissipates -- in three dimensions.

For three dimensions, imagine a latitude - longitude grid on Earth's surface. Each rectangular shaped area within the grid is the end of a column that reaches down to the center of Earth. Of course, the columns taper to a point and have cross sections that are rectangular. The columns themselves are solid angles, and the standard unit of measurement for solid angles is the steradian.