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 85 dB ) by at least a factor of three for cars that are 300 m 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 125 dB ) for a bystander at a distance of 10 m 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).
(b) Suppose that you perceive a sound level equal to x dB when you are situated 150 m from an ambulance siren. Annoyed by the sound of the siren, you start to walk in the opposite direction. How much further do you need to walk in order for the sound level to drop to x−5 dB ?
(c) Suppose an ambulance produces a sound level of 80 dB at a distance of 100 m. How many ambulances would need to be at the same position in order for the sound level at this distance (100 m) to exceed the threshold for hearing damage (125 dB)

Answer 1

For part (a), the power of the siren can take a range of values depending on the desired sound levels at different distances. For part (b), you need to walk a certain distance further in order for the sound level to drop by 5 dB. For part (c), the minimum number of ambulances needed to exceed the threshold for hearing damage at a distance of 100 m can be calculated.

Step-by-step explanation:

(a) To determine the range of power for the siren, we can use the inverse square law for sound intensity. Since the siren should be at least three times louder than typical street traffic at a distance of 300 m, we can calculate the minimum sound intensity of the siren. Start with the sound intensity of street traffic, which is 10^(-12) W/m^2. Multiply this by three, and then invert it to find the minimum intensity of the siren at 300 m. This will give us the maximum power of the siren. To ensure that the sound level at a distance of 10 m does not exceed 125 dB, we can use the inverse square law again. Start with the maximum sound intensity of the siren and find the maximum distance at which the sound level is 125 dB. This will give us the minimum power of the siren. Therefore, the power of the siren can take a range of values depending on the desired sound levels at different distances.

(b) The sound intensity level decreases as the distance from the sound source increases. To find how much further you need to walk in order for the sound level to drop by 5 dB, you can use the inverse square law. Start with the initial distance and calculate the initial sound intensity level. Then, find the new distance at which the sound level is 5 dB lower. The difference between the initial distance and the new distance will give you the additional distance you need to walk.

(c) To exceed the threshold for hearing damage at a distance of 100 m, the sound level must be at least 125 dB. To calculate the number of ambulances needed, we can use the inverse square law. Start with the maximum sound level of one ambulance and find the maximum distance at which the sound level is 125 dB. Then, divide the distance squared by 100 squared to find the number of ambulances needed. This will give you the minimum number of ambulances required to exceed the threshold for hearing damage at a distance of 100 m.