Question

Party hearing. As the number of people at a party increases ,you must raise your voice for a listener to hear you against thebackground noise. However, once you reach the level of yelling, theonly way you can be heard is if u move closer to ur listener. Modelthe sitution by replacing you with an isotropic point source offixed power P and replacing your listener with apoint that absorbs part of your sound waves. These points areinitially separated by . If the background noise increases by

∆β= 5dB
the sound level at your listener mustalso increase. What separation rf, is then requird??

Answer 1

To maintain the perceived loudness when background noise increases by 5 dB, the separation distance between the sound source and the listener must decrease by the square root of 10.

Step-by-step explanation:

The question involves modeling a situation in which a sound source needs to increase its loudness to compensate for an increase in background noise. In this model, the sound source is represented as an isotropic point of fixed power P, and the listener is a point that absorbs part of the sound waves. When the background noise rises by Δβ = 5dB, we need to determine the new separation distance (rf) that will maintain the same perceived loudness for the listener.

Using the inverse square law for sound intensity, we know that intensity decreases with the square of the distance. To ensure that the sound level at the listener increases by 5 dB, we need to adjust the distance. Given that a 10 dB increase would mean that the sound intensity at the listener's location is 10 times greater, a 5 dB increase is approximately a factor of √10 (or 100.5) times more intense. Thus, to achieve this increase in intensity, the distance between the source and listener must decrease by the square root of 10. If the original distance is r, the new required distance is r/