# Sound intensity of a thunderbolt

• Mulz
In summary, the sound intensity of a thunderbolt 1 km away is 26 dB less than the sound intensity at a distance of 20 km. However, this calculation may not accurately reflect reality as it assumes that the sound dissipates completely at a distance of 20 km, which may not be the case. Factors such as air absorption may play a role in the actual sound intensity at different distances.
Mulz

## Homework Statement

Find the sound intensity of a thunderbolt 1 km away. What sound intensity (dB) is it 1 km away? The thunderbolt can be heard up to 20 km away. The sound is spherical. The air absorbs nothing.

## Homework Equations

$$L = 10 \cdot lg(\frac{I_1}{I_0})$$
$$\Delta L = 10 \cdot lg(\frac{I_2}{I_1})$$
$$I = \frac{p_0 ^2}{2z}$$
$$dim(I) = \frac{P}{4πr^2}$$

## The Attempt at a Solution

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I went by the assumption that the sound dissipates at the distance of 20 km. I used equation 4 and found that

$$I_1 = \frac{p}{4πr_1^2}$$ and
$$I_2 = \frac{p}{4πr_2^2}$$ with r1 being 1 km and r2 20 km. I divided them and got $$\frac{I_2}{I_1} = \frac{r_1^2}{r_2^2} = \frac{1}{400}$$ and implemented this in the second equation and got a difference of 26 dB.

This physically makes no sense. How can it be 26 dB difference at a 19 km difference? Whispering is louder. Assuming the sound is completely gone at 20 km, that would mean it's 26 dB at a distance of 1 km away from the lightning. This is obviously wrong and I cannot see the problem with my calculations.

Mulz said:
This physically makes no sense. How can it be 26 dB difference at a 19 km difference? Whispering is louder. Assuming the sound is completely gone at 20 km, that would mean it's 26 dB at a distance of 1 km away from the lightning. This is obviously wrong and I cannot see the problem with my calculations.
Your calculations look correct. Yes, the answer obviously does not correspond to reality. An assumption was made in this problem that might be unrealistic.

See Table B.2 here: https://ccrma.stanford.edu/~jos/pasp/Air_Absorption.html

Or play with some values here: http://resource.npl.co.uk/acoustics/techguides/absorption/

Last edited:

## 1. What is the sound intensity of a thunderbolt?

The sound intensity of a thunderbolt can vary greatly depending on factors such as distance from the bolt, atmospheric conditions, and the strength of the lightning. However, on average, the sound intensity of a thunderbolt can range from 120-160 decibels.

## 2. How is sound intensity of a thunderbolt measured?

Sound intensity is typically measured in decibels (dB). In the case of a thunderbolt, a special device called a sound level meter is used to measure the intensity of the sound waves produced by the lightning.

## 3. What is the loudest thunderbolt ever recorded?

The loudest thunderbolt ever recorded was in the Midwest region of the United States in 2003. It registered a sound intensity of 176 decibels, which is equivalent to standing near a jet engine during takeoff.

## 4. Can the sound of a thunderbolt cause damage to human hearing?

Yes, the sound of a thunderbolt can be damaging to human hearing, especially at close distances. Exposure to sound intensities above 85 decibels can cause permanent hearing damage.

## 5. How far away can the sound of a thunderbolt be heard?

The sound of a thunderbolt can typically be heard up to 10 miles away, but this can vary depending on the strength of the bolt and atmospheric conditions. In some cases, the sound can travel even further, up to 20 miles or more.

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