This article describes basic concepts and principles concerning how sound propagates from a source to a receiver. This is necessary in order to better understand how pickleball noise may disturb nearby residents and how this noise can be controlled. In previous articles we discussed the general problem of Pickleball & Community Noise, Pickleball Noise Fundamentals, and provide an example showing the effectiveness of Pickleball Sound Barriers. In future articles we will examine some of the so-called low-noise pickleball paddles and balls.
Spreading Losses
It is well known that sound levels reduce as we move farther away from a sound source. Typically, locating pickleball courts as far away as possible from residential areas is the first alternative considered by communities. But how far is “far enough” so as not to disturb residents?
Sound from a point source (such as a pickleball paddle) is assumed to radiate spherically in three dimensions (or radially within a two dimensional plane) in a manner similar to ripples on the surface of a pond (Figure 1). The intensity or amplitude of the wave decreases with increasing distance from the source because the wavefront is being spread over a longer circumference. This phenomenon is also known as “spreading loss”.
The sound intensity as a function of distance from the source reduces following an inverse square relationship:
Where ΔSPL is the change in sound level between points 1 and 2, R1 is the distance from the sound source to location 1 and R2 is the distance from the sound source to location 2. This equation implies a useful “rule of thumb” used by acoustical engineers: doubling the distance from the sound source (i.e., R2/R1 = 2) results in a 6 dB reduction in sound pressure level. The spreading loss relationship is plotted in Figure 4. This shows that the majority of the acoustic energy is attenuated within the first 100 m.
For purposes of illustration, let’s assume that the impact noise from a pickleball paddle is 120 dB at a distance of 1 meter (39 inches). If the ambient (background) noise in a community is 60 dB, how far would the pickleball court have to be so that the pickleball impact noise fades into the background?
Using the inverse square relationship above, we desire a ΔSPL = 60 dB, where R1 = 1. Solving for R2 we find that the distance from the court to the house would need to be 1000 m (3280 ft), or over one-half mile away! Clearly, we cannot rely on distance alone to reduce the amplitude of pickleball impact noise.
Atmospheric Absorption
Impact noise levels can be reduced because the acoustic waves are absorbed by the atmosphere, however, the amount of reduction is not constant across the frequency spectrum. In general, lower frequency sound (below about 1000 Hz) is not absorbed as well as higher frequency sound. For this reason, when loud music is played over long distances outdoors from car stereos, restaurants and clubs, or concerts, we normally hear only the low frequency booming sounds. Assuming that pickleball noise occurs at frequencies below about 1000 Hz, we can assume that the atmosphere will provide (at most) only 1 dB / 100 m of attenuation. If we add atmospheric attenuation (at 1000 Hz) to the spreading loss, we obtain the graph shown in Figure 5. In our example above, if we desire to reduce the pickleball impact noise to 50 dB, the required distance decreases from 1000 m to about 600 m.
In actuality, over long distances sound will interact with the ground, vegetation, and objects that are in the path between the source and the receiver. The sound will therefore be absorbed, reflected, diffracted, or refracted, resulting in a lower SPL by the time it reaches the receiver.
Reflection
Impact noise can reflect off of walls, fences, buildings, trees, etc. that may surround pickleball courts or are positioned in the path between the court and residential units. We are all familiar with how sound echoes off of hard surfaces, such as stone or concrete walls inside enclosed spaces, such as canyons. We can hear echoes because our ears can discern sound reflections with a delay greater than about one-tenth of a second. If sound travels at 1125 ft/sec (343 m/sec), a reflecting wall must be at a distance that is greater than 53 ft (16 m) in order for us to hear a distinct echo. Coincidentally, this is about equal to the distance between fences on opposite sides of a pickleball court.
Reverberation is a special case of reflection, where sound that reflects against the walls within an enclosed space is amplified. An example of this can be seen when comparing sound from a hollow-body acoustic guitar with an un-amplified solid-body electric guitar. Although the magnitude of the string vibration between the two guitars is about equal, the sound volume from the hollow-body acoustic guitar is significantly greater. This is attributed to constructive interference among the reflected sound waves within the hollow-body that increase the wave amplitude.
Pickleball courts that are surrounded by acoustically hard surfaces, such as sound barrier blankets or cinderblock walls may actually amplify low frequency sound because of reflection, reverberation, and constructive interference of the pickleball impact noise. Courts surrounded by such surfaces tend to emit a low frequency “thud” when striking a pickleball. This noise can eventually diffract over the sound barrier and into the environment, causing problems for nearby residents.
Diffraction
When sound waves encounter obstacles or small openings in surfaces, they have the capability of bending around the surface and spreading once they get past the surface or opening. This enables us to hear sounds around corners, barriers and to hear sounds through small openings. Diffraction is more pronounced with longer wavelengths, allowing us to better hear low frequency sounds around obstacles than high frequency sounds (Figure 6). Diffraction is used by acoustic engineers to determine the required height of sound barriers, which may be used outdoors to block traffic noise or noise from pickleball courts.
There are several ways to calculate the amount of noise that diffracts over a barrier. A relatively simple method is to use the Fresnel equation for diffraction over an ideal barrier.:
This principal states that the amount of acoustic noise that can be attenuated by a barrier depends on the difference in path length of the sound going over the barrier verses the distance of the sound going through the barrier (Figure 7).
The path lengths, A, B, & d are calculated based on geometry, yielding the Fresnel number, N. Knowing N, we can estimate the barrier attenuation using the chart below (Figure 8).
The amount of attenuation is different for a moving source verses a stationary source (such as an automobile). Furthermore, the chart indicates that the maximum amount of attenuation from a barrier will be about 25 dB.
Refraction
Refraction involves the bending of sound waves through the atmosphere. If you live near a major highway, you know that at certain times of the day, traffic noises are loud and clear, but at other times, traffic noises are barely audible. Why is that? The answer lies in fact that traffic noise is refracting off of the atmosphere.
During the day, the air is warmest near the surface of the earth and gradually cools with increasing altitude. Under such conditions, sound waves developed on the surface of the earth are bent upwards and are dissipated in the cooler atmosphere. Sound therefore does not “carry” on the surface of the earth over long distances under normal refractive conditions (Figure 9).
During the evenings (in particular) when the sun is setting, the earth may cool faster than the air, causing a warm layer of air above the cool air near the earth. This is commonly known as an inversion layer. Sound waves that are developed on the surface of the earth are bent downwards, making sound carry farther on the surface of the earth (Figure 10). This is the reason that traffic noise might appear to be louder during certain times of the day.
Wind has a similar effect. Wind at the surface of the earth has a lower velocity than wind in the upper atmosphere. Therefore, if wind blows from a sound source to a receiver (i.e., wind is towards the receiver’s face, Figure 10), the sound velocity is greater in the upper atmosphere, causing the sound from the source to refract downwards towards the receiver. If wind blows from a receiver towards the sound source (i.e., wind is towards the receiver’s back, Figure 9), the sound velocity is lower in the upper atmosphere, causing the sound from the source to refract upwards away from the receiver.
Controlling Noise Propagation
Community planners have only limited alternatives to control the propagation of pickleball impact noise. As we have seen above, pickleball courts would need to be located a long distance from residential communities, or they would need to be located in areas where there is already a significant amount of background noise, such as near major highways, transportation hubs, commercial, or industrial areas.
Some researchers have studied the effects of vegetative barriers on traffic noise, but these studies indicate that only a modest amount of sound attenuation is achievable (4 dB), particularly at frequencies in the 250 Hz to 2500 Hz range. The use of vegetation such as trees is somewhat of a two-edge sword, as branches and leaves can re-direct acoustic energy from being transmitted upward into the atmosphere to downwards towards the earth.
The only other alternative to interrupting the propagation of pickleball impact noise into communities is to erect artificial structures, such as sound barriers and walls around pickleball courts. These sound barriers will need to be capable of reflecting and absorbing sound, while being sufficiently high so as to limit diffraction over the top of them.
Future Articles
In our next article, Pickleball Sound Barriers, we will evaluate the effectiveness of sound barriers and absorbers that are commonly used to attenuate pickleball noise. In future articles we will examine the various technologies used by pickleball paddle and ball manufacturers to reduce impact noise.
