Question

Party hearing. As the number of people at a party increases, you must raise your voice for a listener to hear you against the background noise of the other partygoers. However, once you reach the level of yelling, the only way you can be heard is if you move closer to your listener, into the listener’s "personal space." Model the situation by replacing you with an isotropic point source of fixed power P and replacing your listener with a point that absorbs part of your sound waves. These points are initially separated by ri = 1.20 m. If the background noise increases by Δβ = 5 dB, the sound level at your listener must also increase. What separation rf is then required?

Answer 1

Answer:

$\frac{r_i}{1.77} m$

Explanation:

Given that

At starting separated = 1.20m

And the increase in background noise by Δβ = 5 dB, due to which the level of sound also rises

Based on the above information, the separation rf that is needed is shown below:

As we know that

$I_f = I_o \times 10^{\frac{\beta}{10} }\\\\I_f = I_i \times 10^{0.5}\\\\I_f = 3.16 \times I_i\\\\I \alpha \frac{1}{r^2} \\\\\frac{r_i^2}{r_f^2} = 3.16\\\\r_f = \frac{\sqrt{r_i^2}}{{\sqrt3.16}} \\\\= \frac{r_i}{1.77} m$

Hence, the separation r_f i.e. required is  $\frac{r_i}{1.77} m$

We simply applied the above equation so that the correct separation could come