Steam Whistle - Whistle Acoustics - Sound Pressure Level

Sound Pressure Level

Whistle sound level varies with several factors:

• Blowing pressure – Sound level increases as blowing pressure is raised, although there may be an optimum pressure at which sound level peaks.

• Whistle scale – Sound level increases as whistle length/width ratio decreases. A halving of effective length may enable the whistle to tolerate a doubling of absolute pressure resulting in a quadrupling of sound level. Variable pitch whistles vary in both frequency and sound level as scale is changed. The sound level of a very squat 587 Hz whistle recorded at the Boot Hill annual whistle blow in 1994 measured 126 C-weighted decibels at 10 meters. A short six-inch diameter plain whistle sounded 113 dbC at 100 feet whereas a six-inch diameter “organ-pipe” design (much lower in frequency) tested under the same conditions sounded 110 dBC at 100 feet. Such comparative measurements as these were recorded in an acoustic half-space at best, and gas flow rates are unknown.

• Whistle diameter – Sound level increases with whistle diameter, as the sound radiating area increases with diameter. Tests of a sample of 13 single-note whistles ranging in size from one-inch diameter to six-inch diameter showed a sound level increase with diameter of 15 dBC, or about six decibels for each doubling of diameter. A 20-inch diameter Ultrawhistle operating at 15 pounds per square inch gauge pressure (103.4 kilopascals) produced 124 dBC at 100 feet. It is unknown how the sound level of a toroidal whistle would compare to that of a high frequency conventional plain whistle of the same diameter. By comparison, a Bell-Chrysler air raid siren generates 138 dBC at 100 feet. The sound level of a Levavasseur toroidal whistle is enhanced by about 10 decibels by a secondary cavity parallel to the resonant cavity, the former creating a vortex that augments the oscillations of the jet driving the whistle.

• Steam aperture width – If gas flow is restricted by the area of the steam aperture, widening the aperture will increase the sound level for a fixed blowing pressure. Enlarging the steam aperture can compensate for the loss of sound output if pressure is reduced. It has been known since at least the 1830s that whistles can be modified for low pressure operation and still achieve a high sound level. Data on the compensatory relationship between pressure and aperture size are scant, but tests on compressed air indicate that a halving of absolute pressure requires that the aperture size be at least doubled in width to maintain the original sound level, and aperture width in some antique whistle arrays increases with diameter (aperture area thus increasing with whistle cross-sectional area) for whistles of the same scale. Applying the physics of high pressure jets exiting circular apertures, a doubling of velocity and gas concentration at a fixed point in the whistle mouth would require a quadrupling of either aperture area or absolute pressure. (A quartering of absolute pressure would be compensated by a quadrupling of aperture area—the velocity decay constant increases approximately with the square root of absolute pressure in the normal whistle-blowing pressure range.) In reality, trading pressure loss for greater aperture area may be less efficient as pressure-dependent adjustments occur to virtual origin displacement. Quadrupling the width of an organ pipe aperture at a fixed blowing pressure resulted in somewhat less than a doubling of velocity at the flue exit.

• Steam aperture profile – Gas flow rate (and thus sound level) is set not only by aperture area and blowing pressure, but also by aperture geometry. Friction and turbulence influence the flow rate, and are accounted for by a discharge coefficient. A mean estimate of the discharge coefficient from whistle field tests is 0.72 (range 0.69 - 0.74).

• Mouth vertical length (“cut-up”) – The mouth length (cut-up) that provides the highest sound level at a fixed blowing pressure varies with whistle scale, and some makers of multi-tone whistles therefore cut a mouth height unique to the scale of each resonant chamber, maximizing sound output of the whistle. Ideal cut-up for whistles of a fixed diameter and aperture width (including single-bell chime compartments) at a fixed blowing pressure appears to vary approximately with the square root of effective length. Antique whistle makers commonly used a compromise mouth area of about 1.4x whistle cross-sectional area. If a whistle is driven to its maximum sound level with the mouth area set equal to the whistle cross-sectional area, it may be possible to increase the sound level by further increasing the mouth area.

• Frequency and distance – Sound pressure level decreases by half (six decibels) with each doubling of distance due to divergence from the source. This relationship is termed inverse proportional, often incorrectly described as the inverse square law; the latter applies to sound intensity, not sound pressure. Sound pressure level also decreases due to atmospheric absorption, which is strongly dependent upon frequency, lower frequencies traveling farthest. For example, a 1000 Hz whistle has an atmospheric attenuation coefficient one half that of a 2000 Hz whistle (calculated for 50 percent relative humidity at 20 degrees Celsius). This means that in addition to divergent sound dampening, there would be a loss of 0.5 decibel per 100 meters from the 1000 Hz whistle and 1.0 decibel per 100 meters for the 2000 Hz whistle. Additional factors affecting sound propagation include barriers, atmospheric temperature gradients, and "ground effects.”