A loudspeaker, mounted on a tall pole, is engineered to emit 75% of its sound energy into the forward hemisphere, 25% toward the back. You measure an 85 dB sound intensity level when standing 1.5 m in front of and 2.5 m below the speaker.

Psource is 22.56 X 10⁻³ W

Explanation:

Given-

Sound Intensity level, β = 85dB

Position at which intensity is measured, x = 1.5m

y = 2.5m

We know,

Intensity, I = Power (P) / Area (a)

For a spherical wave, the intensity at distance r is:

I = P (source) / 4πr²

The sound intensity level in decibels is expressed as:

β = (10dB) log₁₀ (I/I₀)

where, I₀ = 1 X 10⁻¹² W/m²

To calculate the distance r from the source to the position at which the Intensity is measured.

It is given that 75% of the energy is emitted in forward hemisphere. So,

P' = 75% Po/50%

P' = 1.5P₀

By plugging in the values in equation I = P (source) / 4πr², we get

Thus, Psource is 22.56 X 10⁻³ W

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