Question

suppose that you would like to have a siren which is loud enough that its intensity will exceed that of typical street traffic (which has a sound level of ) by at least a factor of three for cars that are away from the siren source. however, you also do not want it to be so loud that it can cause hearing damage (caused by a sound level above ) for a bystander at a distance of from the siren source. what is the range that the power of the siren can take so that it is consistent with these requirements? (you may neglect damping/attenuation).

Answer 1

To determine the power range for a siren consistent with safety requirements, one must calculate using the decibel scale of sound intensity, considering the levels of street traffic noise and the threshold for hearing damage. Exact values for these levels are needed to provide a specific range.

Step-by-step explanation:

The question asks about determining the power range for a siren, taking into account the sound level above which it can cause hearing damage and being adequately louder than the sound of typical street traffic. Given that high noise exposure is hazardous to hearing, it's essential to compute an acceptable power range for the siren that balances effectiveness with safety. We must use the logarithmic decibel scale of sound intensity to compare the sound levels. The decibel level of typical street traffic and the threshold for hearing damage are not provided explicitly in the question, which requires them to answer accurately. Nevertheless, the general concept involves using the sound intensity level formula S = 10 × log(I / I0) where S is the sound level in decibels (dB), I is the intensity of the sound, and I0 is the reference sound intensity, typically 1×10⁻¹² W/m² in air.