Final answer:
When 39 identical speakers are used together, each producing 91.5 dB, they create a combined sound level of approximately 107.4 dB in the front row area, calculated using a logarithmic relationship between sound intensity and decibels.
Step-by-step explanation:
To determine the sound level produced by a wall built out of 39 identical speakers, we need to use the concept of sound intensity levels and decibels (dB). When multiple sources of sound that are identical and coherent (such as the speakers in a rock band) are combined, their intensities add up. However, the relationship between sound intensity and decibels is logarithmic, not linear.
The formula for calculating the increase in decibels when the number of sound sources is increased is given by:
ΔdB = 10*log(N)
where ΔdB is the change in decibels and N is the number of sound sources (speakers in this case). If a single speaker produces a sound level of 91.5 dB, and there are 39 speakers in total, the increase in decibels due to the additional speakers is calculated as follows:
ΔdB = 10*log(39) ≈ 10*1.59 ≈ 15.9 dB
Therefore, the total sound level produced by the whole wall of speakers would be:
Total sound level = Sound level of one speaker + ΔdB
Total sound level = 91.5 dB + 15.9 dB ≈ 107.4 dB
So, a rock band uses a wall built out of 39 identical speakers to create a combined sound level of approximately 107.4 dB in the front row area.