# Speed of Sound vs. Distance

1. Oct 17, 2008

### Mangover

I am currently enrolled in a driver / operator class for my fire department and a statement that was written in our text books has been bothering me. " If a fire apparatus is traveling at 40 miles per hour the siren can be heard at a distance of 300ft. However, if a fire apparatus is traveling at 60 miles per hour the siren can only be heard from a distance of 12 ft." I have always been told that the faster an Emergency vehicle goes the less effective the sirens become... to me that is questionable and this drastic falling off of audible sound is almost unbelievable, especially at such low speeds. I'm not sure exactly how loud the siren is that the book is referencing only that this statement is unrealistic but hey i could be wrong and probably am. If anyone could explain to me how they got this and if they are even right i would greatly appreciate it. I have looked everywhere and can not find any relation to speed, sound, and audibility.

This quotation is taken from a California State Driver Operator Handbook that is a required read to become state certified.

2. Oct 17, 2008

### Danger

Welcome to PF, Mangover.
I'm not really a scientist, but this sounds weird to me. We have a lot of emergency vehicles in my area, and I can sure as hell hear them coming from a couple of miles away at 110 kph (70 mph). Even if one is coming toward me on the highway, for a combined closing speed of 140 mph, with my windows rolled up, I can hear it at least 1 km away. I definitely notice the red/blue shifts as it passes, and a higher volume at closer separation, but 12 feet is just nuts. You can hear a cat fart at that range, no matter how fast it's moving.

3. Oct 17, 2008

### GAGS

Nice question

Hi mangrover, actually i dont know whether i am right but to me both statements are true:
You are saying
40miles/hour--------> 300ft
60miles/hour--------> 12ft.
I am not taking mathematical calculations here,but if you see in first case the sound waves are heard at large distance compared to second one, and sound in second case when will reach to 300ft is so attenuated(intensity reduced) that fewer peoples will be able to hear it.
Moreover in a circular perimeter of 300ft radius (as sound waves are going in all possible directions),large no. of peoples will be able to hear it as compared to no.of peoples in 12ft radius.
I hope it helps.
Thanks

4. Oct 17, 2008

### Mangover

What????

Im kinda looking for the formula that shows the relation between an objects speed and the distance it can be heard if it were emitting a steady sound. I understand It can be heard in a circular direction, but the notion that it is compressed so greatly at such slow speeds is odd to me.

5. Oct 18, 2008

### Loren Booda

I think that the sound intensity S would vary as S/Sv=0=(1-(v/340[m/s]))2, where v is the velocity of the siren relative to the observer who hears the siren head on. For v=0, S/Sv=0 would be maximum. For v=340[m/s], S/Sv=0 would be zero, as expected for a horizon. The squaring would arise from the contraction of source power by the Doppler effect.

Since the sound level B=(10dB)log(S/Sv=0), the reduction in B due to v being equal to, e. g., 340[m/s]/2 seems a measly .6dB.

Where did I go wrong?

6. Oct 18, 2008

### schroder

I don’t believe the data was computed with a mathematical equation; rather, it was compiled by empirical testing in the field and involves things such as masking noise, car sound-proofing as well as human reaction times to the siren.

You may find this useful:
A US Department of Transportation (DOT) report (Washington, DC, US Department of Transportation, National Highway Traffic Safety Administration, publication No. DOT-TSC-OST-77-38, 1977) showed that over a siren's effective frequency range, the average signal attenuation (through closed-windowed automobile bodies combined with typical masking noise) resulted in a maximal siren effective distance of siren penetration of only 8 to 12 meters at urban intersections. Only modest improvement in the situation occurred at suburban intersections and straight-ahead highway conditions. These findings have been corroborated, and from the data a maximum safe entry speed of 10 mph (15 km/hr) for intersections is recommended . The Department of Transportation report concluded that sirens will never become an effective warning device.

7. Oct 18, 2008

### Naty1

I agree the text is misleading at best, likely incorrect....

Sound travels at around 1088 ft per second in typical ambient air temperature and humidity... separately, At 60 mph an emergency vehicle covers about 88 ft/sec....

So even a FAST vehicle is moving only about 88/1088 about 8% the speed of sound...

so the frequency might vary about 8%, meaning the tone, due to doppler shift, but that should have little if any effect on the effective range....if anything moving the sound source in the direction of propagation (via a moving vehcile) should increase it's energy and therefore it's range....not decrease it...but the time between detection by an observer and passage of the vehicle might decrease....

I agree with you, the implication in the text appears incorrect based on the characteristics of the two speeds....maybe they left off some zeros!!!!

I can sure hear police cars a block or two away in my car with the radio on....thats a lot more than 300 ft....

8. Oct 20, 2008

### jablonsky27

I think that the distance the handbook refers to is the distance between the fire engine moving at 60mph and another vehicle(say a car) thats travelling at roughly the same speed in front of it which needs to get out of the fire engines way.
If you are stationary, then you can hear the fire engine from a mile away - its a non issue.

9. Oct 21, 2008

### Naty1

Schoder has the right idea....there are so many variables it's likely that tests rather than theory and equation determine meaningful results. For example, a wind in the wrong direction will greatly attenuate a sound signal, reflections from buildings or trees as well....I'd guess the relative speed of a vehicle, as I posted above, has little effect compared with practical situations encountered in the real world...

10. Oct 21, 2008

### brewnog

The fire engine travelling at 60mph with the sirens turned off is a great deal louder than when travelling at 40mph; the extra noise from the engine, exhaust and wind rush will do a pretty good job of drowning out the siren to some extent.

11. Oct 21, 2008

### rbj

i work in audio signal processing, i understand a healthy amount of acoustical physics, even though i cannot claim to be a practitioner of acoustics, but that quote from the California State Driver Operator Handbook seems highly suspect to me. if the sound source is moving towards the listener, i can see no mechanism whatsoever that such motion would attenuate the sound. you might not hear it for as long, but the sound intensity at some instant of time would still be inversely proportional to the square of the distance and, as far as i know, not some function of the speed.

12. Oct 22, 2008

### kyotasha

I understand the mathematics behind the Doppler effect and whatnot, but i dont think people are accounting for a real world scenario. First off, the speed of sound in a standard barometric pressure, humidity (i don't remember the exact value of these), and open space is 343 m/s. but you throw in a different pressure, possibly rain, and buildings (like the US DOT did in its study, I'm sure) and you realize that sirens are not always effective, and quite possibly could be overcome by ambient noises and environmental situations. I believe that going through a downtown intersection, a siren will NOT be heard and the direction from which it is coming will not be identified from much further than a block away (if not less).
But as far as specifically stating the range is 12 feet, these previous posts are right, and i can not imagine a way of calculating this value.