Question

while attending a concert you notice that at a distance of 10m from the speaker, the intensity level is 80dB. Wanting to not destroy your ears, you walk away to a distance of 30m. What is the intensity level at your new location?

Answer 1

When moving from 10m to 30m away from a concert speaker, the intensity level decreases. Starting from 80dB at 10m, the new intensity level at 30m is approximately 70.4 dB due to the inverse square law related to distance and sound intensity.

Step-by-step explanation:

The student is asking about the change in sound intensity level as they move from 10m to 30m away from a concert speaker. Sound intensity level drops off as the square of the distance from the source, according to the inverse square law. Given that the initial intensity is 80dB at 10m, the intensity will decrease as you move further away. The calculation of the new sound intensity level at 30m involves this inverse square law:

Intensity level drops by 20 dB when the distance is increased by a factor of 10. Since the distance is tripled (going from 10m to 30m), the intensity level will drop by:

20*log10(3) ≈ 20*0.48 ≈ 9.6 dB

So the new intensity level at 30m would be:

80 dB - 9.6 dB ≈ 70.4 dB

This shows a significant reduction in the sound intensity level, which would indeed be safer for hearing over longer periods.