Final answer:
The intensity level of each of the ten violins, when playing simultaneously to give a total sound level of 70 dB, is approximately 60 dB. The sound level in dB has a logarithmic relationship with intensity, where each tenfold increase in intensity corresponds to a 10 dB increase in sound level.
Step-by-step explanation:
The question is asking to determine the intensity level of each violin if ten violins playing together produce a sound level of 70 dB. The concept being applied here is related to sound intensity level and its logarithmic nature. Sound levels in dB add logarithmically rather than arithmetically, which means that a 10 dB increase represents a sound that is ten times more intense, while each doubling of such intensity only increases the sound level by about 3 dB.
To solve for the intensity level of one violin, we know that ten violins create a sound level of 70 dB. If we were to add another group of ten violins playing at this same level, we would only increase the sound level by about 10 dB, which would make the total 80 dB. Since we have ten violins, each additional violin contributes about 1 dB to the total, assuming the sound intensity of each is equal. Therefore, we can calculate:
- 70 dB - 10 dB (since 10 violins contributing equally) = 60 dB
Thus, each individual violin has a sound level of approximately 60 dB.