Question

Someone with perfect pitch and an encyclopedic knowledge of sirens can determine how far away an ambulance is and how fast it is traveling at based solely off the loudness and pitch of the ambulance's siren, respectively.

a) How can the distance be determined from the loudness of the siren? Are there limitations to the accuracy of this determination?

b) How can the speed be determined from the pitch of the siren? Are there limitations to the accuracy of this determination?

Answer 1

a) The loudness of a sound is determined by its intensity. The intensity of sound follows the following relation-

Here,

I = Intensity

r = distance of the observer from the source

So, from the above dependence, we can see that we can easily determine the distance between us ad the source of the siren by measuring it's intensity i.e. loudness.

Limitation- We should know the intensity of sound from one distance in able to measure the other distances based on the intensity. So, an initial condition is required to use this method.

b) The pitch of a sound corresponds to the frequency of the sound. The frequency of sound changes based on the velocity of the source of the sound. This effect is called the Doppler effect of sound. Using the Doppler effect relation, we can easily find the speed of siren source by measuring the shift in the pitch of the siren as it reaches us.

Limitations- We need to know two things to use this method. First is, the actual pitch of the siren that the source emits. From that, we can find the change in pitch by Doppler effect. Second, we need to know the velocity of sound in the air around us. This velocity might change depending on the air composition around us, which can generate some error in our calculation.