5. Consider two sources of sound (speakers for example) that are located on the

Question

5. Consider two sources of sound (speakers for example) that are located on the x-axis, each emitting sound uniformly in all directions. There are no echoes and interference isn?t the point of this problem. One source sits at the origin and the other sits at x=+ 186.0 m. The source that is sitting at the origin is 4 times as powerful as the source sitting at +186.0 m. a) Without calculating anything, think about it, is there any place along the x-axis to the left of the source at the origin, short of infinity, where the sound intensities could be the same? Explain briefly. b) Without calculating anything, think about it some more, is there any place along the x-axis between the two sources where the sound intensities could be the same? Explain briefly. c) Think about it one more time; is there any place along the x-axis to the right of the source at + 186.0 m, short of infinity, where the sound intensities could be the same? Explain briefly. d) Find the positions along the x-axis where the two sounds from the two sources would be equal in intensity.

Explanation / Answer

a) No.

Intensity = Power/Area

when we take any on the -x axis it is close to the source of sound placed at origin. an this source is power full.

so, at any point intensity due to the source placed at origin always greater.

b) yes.

when we take a point close to seond source, the intensities will be equal.

c) yes.

when we go away from second source at a particular pioint the two intensisties would be same.

d)

Let x is the distance from where the two intensities are same.

beyound second source.

I1 = I2

4*P/4*pi*x^2 = P/4*pi*(186 - x)^2

4*(186 - x)^2 = x^2

on solving the above equation we get,

x = 124 m and 372 m <<<<<------------Answer

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