Question

How can I calculate the distance that sound wave can go, I have a sound with 60 db how can I know the end point I can hear in, I know that it changes determine on temperature and so many things can I know how to calculate it?

Answer 1

Calculating the exact distance that a sound wave can travel based on its intensity (expressed in decibels) can be a complex task due to various factors involved. However, you can make a rough estimation using the Inverse Square Law, which describes the relationship between the intensity of a sound wave and the distance from its source.

The Inverse Square Law states that the intensity of a sound wave decreases in proportion to the square of the distance from the source. In other words, doubling the distance from the source results in a quarter (1/2^2) of the original intensity.

Here's a step-by-step approach to estimate the distance at which a sound wave with a given intensity (in decibels) becomes inaudible:

1. Determine the reference distance: Select a reference distance at which the sound intensity is known. For example, you might know the intensity (in decibels) of the sound wave at a distance of 1 meter from the source.

2. Calculate the intensity difference: Determine the difference in decibels between the reference distance and the desired distance. For instance, if the sound intensity at 1 meter is 60 dB and you want to find the distance where it becomes inaudible (let's say 30 dB), the intensity difference would be 60 dB - 30 dB = 30 dB.

3. Apply the Inverse Square Law: Calculate the ratio of the intensity difference in decibels and apply it to the Inverse Square Law. Since the intensity decreases with the square of the distance, you can use the formula:

   (Distance at reference intensity)² / (Desired distance)² = 10^(Intensity difference in dB/10)

   Rearrange the formula to solve for the desired distance:

   Desired distance = (Distance at reference intensity) / sqrt(10^(Intensity difference in dB/10))

   Plug in the values to calculate the distance.

Keep in mind that this estimation assumes ideal conditions and does not account for factors such as absorption, reflection, scattering, and environmental conditions. Additionally, the Inverse Square Law may not accurately represent the behavior of sound waves in certain scenarios.