# Sound Loudness: Increase of 13.98 dB

• fghtffyrdmns
In summary, sound loudness is measured in decibels (dB), and an increase of 13.98 dB means a perceived doubling of loudness. Common examples of a 13.98 dB increase in loudness include a car horn, city street, lawnmower, or loud conversation. However, a 13.98 dB increase can be harmful to our ears and there is a limit to how loud sound can become before it becomes uncomfortable or distorted. This limit is known as the "threshold of discomfort" and varies from person to person. It is important to protect our ears from loud noises to prevent hearing damage.
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## Homework Statement

How many decibels does the loudness of a sound increase if its intensity increases 25 times?

## Homework Equations

$$dB = 10 log\frac{I_{b}}{I_{a}}$$

## The Attempt at a Solution

$$\frac{I_{b}}{I_{a}} = \frac{25}{1}$$

$$dB = 10 log\frac{25}{1}$$
$$dB = 13.98$$

Correct.

+ 10 log(25)
dB = 13.98 + 10(1.39794)
dB = 27.98

The loudness of the sound would increase by 27.98 dB if its intensity increases 25 times. This is because the decibel scale is logarithmic, meaning that a 10-fold increase in intensity corresponds to a 10 dB increase in loudness. Therefore, a 25-fold increase in intensity would result in a 25 dB increase, which when added to the original loudness of 13.98 dB, gives a total increase of 27.98 dB.

## 1. How is sound loudness measured?

Sound loudness is measured in decibels (dB), which is a unit that represents the intensity of sound. The higher the decibel level, the louder the sound.

## 2. What does an increase of 13.98 dB mean for sound loudness?

An increase of 13.98 dB means that the sound intensity has increased by a factor of 10, which results in a perceived doubling of loudness. This is known as a "doubling factor" in sound measurement.

## 3. What are common examples of sounds with a 13.98 dB increase in loudness?

A 13.98 dB increase in loudness can be equivalent to the sound of a nearby car horn or a busy city street. It is also comparable to the sound of a lawnmower or a loud conversation.

## 4. Is a 13.98 dB increase in loudness harmful to our ears?

Yes, a 13.98 dB increase in loudness can be harmful to our ears if we are exposed to it for a prolonged period or at close proximity. It is important to protect our ears from loud noises to prevent hearing damage.

## 5. Can sound loudness be increased indefinitely?

No, sound loudness has a limit and cannot be increased indefinitely. As the loudness increases, the sound may become distorted or uncomfortable to listen to. This is known as the "threshold of discomfort" and varies from person to person.

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