How far can a siren be heard? Sound propagation and coverage design for community warning

A siren is the last link in a flood warning chain. Everything upstream, the sensors, the telemetry, the decision rule, is wasted if the people at risk do not hear the alarm. "How far can a siren be heard?" has no single answer, because the answer depends on the siren, the air, the ground, the hills and the noise of the place. This article sets out the acoustics that govern it, using a published U.S. Nuclear Regulatory Commission procedure for analysing siren systems, worked numbers, and a practical method for planning coverage in a hill valley.

The listener-level equation

The NRC procedure, Procedures for Analyzing the Effectiveness of Siren Systems for Alerting the Public, builds the outdoor sound level at a listener from the siren's rated output, minus a set of attenuations [1]:

L_listener = L_siren − A_d − A_s − A_air − A_atm

• L_siren is the rated sound pressure level at a reference distance of 100 ft (about 30.5 m).
• A_d is the distance attenuation, from spreading of the sound.
• A_s is the shielding attenuation from hills, buildings and other barriers.
• A_air is air absorption.
• A_atm is the effect of wind and temperature gradients.

The procedure assumes the siren is mounted about 50 ft (15 m) above the ground and the listener is 5 ft (1.5 m) above the ground, unless better information exists [1]. We use the same structure below. The siren rating in our examples, 120 dB at 30.5 m, is an illustrative figure for a high-output outdoor siren, not a specification of any product.

Distance: 6 dB every time you double it

Sound from a point source spreads over a sphere, so intensity falls with the square of the distance. The NRC procedure calculates distance attenuation beyond 100 ft "by assuming sound propagation from an acoustic point source with a reduction of 6 dB per distance doubled" [1]:

A_d = 20 · log10( d / d0 )        (d0 = 30.5 m)

Adding air absorption of about 3 dB per kilometre (see below), a 120 dB siren at 30.5 m gives, in open, flat terrain with no wind effects:

Read the table as a ceiling. A level of 70 dB is reached at about 3.2 km in this idealised case and about 1.7 km with an extra 10 dB of real-world loss. The distances at which a given level is met are:

A doubling of range needs 6 dB more output, or about four times the acoustic power. That is why more sirens placed closer to people are usually better than one very loud one.

Air absorption: why mid-frequency tones carry

Air absorbs sound, and absorbs high frequencies far more than low ones. ISO 9613-1 gives absorption coefficients that depend on frequency, temperature and humidity. At 10 °C and 70 % relative humidity, the values in dB per kilometre are about [2]:

The NRC procedure's own table at 500 Hz, in its units, ranges from about 0.6 to 1.2 dB per 1,000 ft (about 2 to 4 dB/km) across the temperatures and humidities it considers [1]. This is why a siren tone intended to carry sits in the low hundreds of hertz, and why the NRC analysis is done in the one-third-octave band centred at 630 Hz [1]. A shrill tone is audible nearby and dies quickly with distance.

Terrain: hills and buildings cast acoustic shadows

A hill or building between the siren and the listener blocks the direct path, and sound reaches the listener only by bending over the top. How much it is reduced depends on the Fresnel number N, which compares the extra path length over the barrier with the wavelength:

N = 2 · δ / λ          δ = (A + B) − d     λ = c / f

where A + B is the shortest path over the barrier and d the straight-line distance. At 630 Hz the wavelength is 0.544 m. The NRC procedure estimates the shielding attenuation of a rigid barrier from a point source with:

A_s = 20 · log10( √(2πN) / tanh √(2πN) ) + 5 dB      (for −0.2 < N < 12.6)
A_s = 24 dB                                           (for N > 12.6: the practical limit)

and caps shielding at 24 dB "based upon a large body of experimental data" [1]. Worked values for the path difference over a barrier:

A spur of ground only 1 m above the line of sight between a siren and a house takes about 19 dB off the level there, which is roughly the same as ten times the distance. This is the central problem in river valleys: a siren placed at one bend may not reach the next village behind a spur, however close it is. Terrain, not distance, often decides coverage in the hills.

Wind and temperature: the weather changes the map

Sound travels in curved paths when the wind or temperature varies with height. Downwind, or when cool air lies near the ground (an inversion, common on still nights and early mornings in valleys), sound is bent downward and carries further. Upwind, or when the ground is warm, it bends upward and leaves a shadow near the ground. The NRC procedure includes an adjustment for these effects that depends on the direction from the siren relative to the wind and on the wind and temperature gradients [1]. Plan for the unfavourable case: the siren that is audible in the evening calm may be short of range in the afternoon wind. Both conditions occur on the day of a flood.

Being heard: detection against background noise

The ear picks out a tone from noise within a narrow band of frequencies around it. The NRC procedure therefore compares the siren level with the background noise in the one-third-octave band centred on 630 Hz, and sets its alerting criterion as a signal 9 dB or more above the minimum background noise during the siren's operating period [1]. The relevant background is the quietest level that occurs, because people hear the siren "between the cracks" of louder interference [1].

What sets background noise depends on the place. Traffic dominates in towns and along roads. In rural areas the NRC data set lists sources such as a rushing stream, wind in trees, birds, farm animals and dogs [1]. That last point deserves attention in a river valley: moving water is itself a source of broadband noise, loudest near rapids and in monsoon flow, which is when you need the siren. Siting the siren away from the loudest part of the river, and choosing tones and levels with that noise in mind, are part of the design. A quiet village at night, away from the river and from roads, is a low-noise environment, and a siren is detected easily there if the path is clear. Measure the minimum background at your sites, at the times you care about, instead of assuming it.

Indoors: the weakest point of an outdoor siren

At night, in heavy rain, most people are inside. A building reduces the sound. The NRC procedure adopts figures for the 500 Hz octave band, summarised from Society of Automotive Engineers data, for residential structures [1]:

A siren heard at 70 dB outside is therefore about 54 dB inside a cold-climate home with the windows open, and about 43 dB with them closed, falling toward the level of ordinary indoor sounds. Housing in your valleys will differ from the housing in those studies, so measure it. The conclusion is robust, though: an outdoor siren is built to alert people who are outside, and it cannot be relied on alone for people who are indoors and asleep. Pair it with channels that reach inside: mobile alerts (in India, the national alert platform SACHET delivers geo-targeted SMS using the Common Alerting Protocol [3]), phone calls to local leaders, and volunteers who go door to door.

A method for planning coverage in a valley

1. Map the people. Where are the houses, the fields, the bridges and the paths, and when are people outdoors?
2. Choose candidate siren sites with a clear view of as many houses as possible, away from the loudest water noise, on stable ground and with solar exposure.
3. Compute the level at each listener point with the equation above, using terrain data to find the shielding for each hill and building in the path.
4. Take the worst case: upwind and warm-ground conditions, closed windows if indoor alerting is the aim.
5. Compare with the target: background plus at least 9 dB in the 630 Hz band outdoors. Emergency-planning criteria around U.S. nuclear plants have used 70 dBC in densely populated areas and 60 dBC in less dense ones [4]; local targets should come from measurement.
6. Add or move sirens until the gaps close. Several moderate sirens often cover a winding valley better than one loud one.
7. Test in the field with a calibrated sound level meter at a sample of points, in daytime and at night, and in wind and calm. Record the results and tune.
8. Retest each season, and after any change to the siren, the ground or the housing.

Safety, tests and care

Levels near a high-output siren are far above those that damage hearing, so set a safe distance around it and use hearing protection when testing nearby. Plan a routine test schedule that people know about, so a real alarm is not mistaken for a test, and use remote monitoring of battery, solar charging, connectivity and last communication so a failed siren is found before the flood and not during it.

Where ClimMaTech fits

Rakshak is our last-mile warning device: a solar-powered siren with a beacon and voice messages, available in 1, 2 or 4-direction layouts with configurable tones and patterns, triggered over GSM, LoRa or VSAT through an open API. Its device health reporting covers power status, battery level, solar charging, connectivity and last communication. The Rakshak Control Centre, coming soon, is designed to accept CAP alerts and manage siren networks. Siren output and coverage depend on the configuration chosen for each site, so we plan layout with the acoustics above, including terrain and local noise. See reaching communities with GSM, LoRa and sirens, early warning dissemination and river monitoring in hill catchments.

References

1. D. N. Keast and others, Procedures for Analyzing the Effectiveness of Siren Systems for Alerting the Public, NUREG/CR-2654 (PNL-4227), prepared for the U.S. Nuclear Regulatory Commission (1982). Digital library.
2. ISO 9613-1:1993, Acoustics: Attenuation of sound during propagation outdoors, Part 1: Calculation of the absorption of sound by the atmosphere (coefficients as tabulated in sengpielaudio.com).
3. MicroSave, Turning the tide: how India's SACHET system is reshaping disaster preparedness. microsave.net.
4. U.S. Nuclear Regulatory Commission, documents on prompt alert and notification siren design criteria. nrc.gov.

Worked values are computed from the relations in the NRC procedure and ISO 9613-1, with the stated illustrative siren rating (120 dB at 30.5 m) and assumptions. Real coverage depends on the siren, the site and the weather, and must be confirmed by measurement.