Problem 2.4 (7 points): For sound waves, we said that the energy carried by the
ID: 1539366 • Letter: P
Question
Problem 2.4 (7 points): For sound waves, we said that the energy carried by the sound decreased with distance, giving I = P . Surface waves spreading out 4R2 away from a single point source obey a similar sort of equation, based on the same logic, but there is a crucial change: they don’t disperse into three dimensions, only 2. Describe what has to change to describe the intensity of a surface wave that spreads out in a 2 dimensional plane instead of out in any possible direction in 3 dimensions. What is the equation describing how I depends on R on the ocean’s surface? This problem will involve a very small amount of math.
Explanation / Answer
In three diemsnions, Intensity I = Power.Area
= I/(4*pi*R^2) (here 4*pi*R^2 is the surface area of a sphere with radius R)
In two dimensions,
Intensity = power/Area
= P/(pi*R^2) <<<<<<<<------------Answer
because, as the wave progates on the surface radius of the circle increases.
we know, the area of circle, A = pi*R^2
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