Question

you are attempting to design an ambulance siren. you would like the siren to be distinct enough that it will be clearly audible in case of emergency, but not unnecessarily disruptive. (a) 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

In designing an ambulance siren, it is important to ensure that the siren's sound intensity is above the typical street noise level yet remains below the threshold that can cause hearing damage. The power of the siren must be carefully calculated to meet these criteria without accounting for sound damping/attenuation, and considerations for the Doppler effect should be included in the design process.

Step-by-step explanation:

When designing an ambulance siren, it is crucial to consider the parameters that will ensure the siren is audible above typical street noise but not harmful to the bystanders. This involves calculating the sound intensity levels and understanding the relation between the sound power, the distance from the source, and the perceived loudness (decibels, dB).

Sound intensity is inversely proportional to the square of the distance from the source, and the decibel level is a logarithmic measure of sound intensity. The loudness or sound level in dB can be calculated from the sound power using the formula L = 10 log(I/I₀), where I is the sound intensity and I₀ is the reference intensity. To surpass the sound of traffic by a factor of three without causing hearing damage at a distance of, say, 1 meter, the power of the siren must be calculated while considering the thresholds for safe listening according to occupational health guidelines.

The design of the siren should also include consideration for the Doppler effect, which causes the frequency of the siren to vary for observers depending on whether the ambulance is approaching or receding from them. The Doppler effect illustrates how the pitch of the siren changes as an ambulance moves past an observer.