Question

designing a siren 4 points possible (graded) 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). maximum power: unanswered

Answer 1

When designing an ambulance siren, its power must allow the sound to be heard clearly over street traffic but not so high as to cause hearing damage at the minimum bystander distance. The power range can be calculated using the decibel levels, the factor increase over street traffic noise, and the inverse square law of sound intensity.

Step-by-step explanation:

When designing a siren for an ambulance, the siren's power must be within a certain range to be heard over typical street traffic without causing hearing damage to nearby bystanders. We can consider the decibel levels representative of typical street noise and the threshold for hearing damage to determine the power requirements of the siren. If the street traffic is at a certain decibel level, the siren needs to be louder by a factor of three, yet it must remain below the level that would cause hearing damage at the specified distance.

The intensity level of a sound is proportional to the logarithm of the ratio of its intensity to a reference intensity. Since the goal is to exceed street traffic noise by at least a factor of three, we calculate the corresponding increase in decibels for this ratio. To prevent hearing damage, the siren's intensity should not exceed the decibel level that is considered harmful at the closest distance a bystander might be.

To find the maximum power of the siren, we can use the inverse square law of sound intensity. This law states that the intensity is proportional to the power of the source and inversely proportional to the square of the distance from the source. The power range of the siren then can be calculated considering the minimum distance a bystander might be and the required sound intensity increase over ambient levels.