Question

Review Conceptual Example 8 as background for this problem. A loudspeaker is generating sound in a room. At a certain point, the sound waves coming directly from the speaker (without reflecting from the walls) create an intensity level of 81.7 dB. The waves reflected from the walls create, by themselves, an intensity level of 67.4 dB at the same point. What is the total intensity level? (Hint: The answer is not 149.1 dB.)

Answer 1

The loudspeaker is an example of incoherent source.

Given in the problem -

Intensity level LA = 81.7 dB

Intensity level LB = 67.4 dB

Therefore, total intensity level at the same point will be equal to the addintion of two incoherent sound pressure levels -

LA and LB = 10×log [10^(LA/10)+10^(LB/10)]

= 10×log [10^(81.7/10)+10^(67.4/10)]

= 10×log [ 147910839 + 5495409 ]

= 10×log (153406248) = 81.85 dB

Therefore, the total intensity level = 81.85 dB (Answer)