Hemispherical Sound Propagation Calculator

In the field of Physics, particularly Acoustics, the propagation of sound is a fundamental study area. Hemispherical sound propagation, specifically, refers to the dispersion of sound energy in a half-spherical (or hemispherical) pattern from a point source. It is especially relevant in outdoor environments where the ground can serve as a reflective surface. This tutorial will discuss the main parameter related to hemispherical sound propagation: sound pressure. We will introduce the fundamental formula associated with this concept, its derivation, its application in real life, and the key individuals involved in its development.

Sound Pressure At Hemispherical Free Field Calculator
Hemispherical Sound Propagation Calculator Results
Sound Pressure Level = dB
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Example Formula

The primary formula related to hemispherical sound propagation involves calculating the sound pressure level at a specific distance from the source. It is as follows:

LP2 = LP1 - 20 log10(r2/r1)


  1. LP1: Represents the sound pressure level at distance r1 from the source.
  2. LP2: Represents the sound pressure level at distance r2 from the source.
  3. r1, r2: Represent the initial and final distances from the source, respectively.

Who wrote/refined the formula

This formula is a variant of the general equation for sound pressure level drop with distance, commonly used in acoustics. It is based on the inverse-square law, a principle that was initially applied to light and sound propagation by scientists like Isaac Newton and Robert Hooke in the 17th century.

Real Life Application

Hemispherical sound propagation concepts are essential in the design and planning of outdoor concerts and public address systems. By understanding the behavior of sound propagation, sound engineers can optimally place speakers and microphones to ensure sound coverage and minimize noise pollution.

Key individuals in the discipline

Many scientists have contributed significantly to our understanding of sound and its propagation. Robert Hooke and Isaac Newton in the 17th century were among the first to apply the inverse-square law to sound propagation. Later, in the 19th and 20th centuries, scientists like Lord Rayleigh and Wallace Clement Sabine further refined our understanding of acoustics and sound propagation.

Interesting Facts

  1. Hemispherical sound propagation is also observed in underwater acoustics, where sound energy spreads out in a hemispherical pattern due to the water surface's reflection.
  2. Understanding sound propagation has led to the design of advanced sound systems that have revolutionized the music and entertainment industry.
  3. The principles of sound propagation are also used in medical imaging technologies like ultrasound.


The study of hemispherical sound propagation is integral to our understanding and manipulation of sound in various environments. Its practical applications are vast and have substantial implications in fields ranging from entertainment to medical technology. The understanding and application of this physics principle have contributed significantly to advancements in these sectors.

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