The intensity of the sound wave

In summary, the intensity of a sound wave is a measure of the amount of energy that passes through a given area per unit time. It is typically measured in decibels (dB) and can be affected by factors such as distance, frequency, and medium. The intensity is directly proportional to its perceived loudness, meaning that as it increases, the sound will be perceived as louder. However, high intensity sound waves can also be harmful, causing damage to the ears and potential hearing loss if exposed to for long periods of time.
  • #1
hidemi
208
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Homework Statement
The speed of sound in air in 340 m/s, and the density of air is 1.2 kg/m^3. if the displacement amplitude of a 440 Hz sound wave is 10μm. what is the intensity of the wave?

Ans: 32 W/m^2
Relevant Equations
I = 1/2 ρvR²w²
I = 1/2 ρvR²w²

I = 1/2 *1.2kg/m³*340m/s*(10 x 10^-6m)²*(2π*440/s)²

I = 0.16 W/m²

This is my answer which does not match the given answer. Am I doing wrong?
 
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  • #2
32W/m2 is hearing damage in a matter of seconds. Even 0.16 for 30 min is ill-advised.
From a rough calculation, I agree with your answer.
 
  • Informative
Likes hidemi

1. What is the definition of intensity in sound waves?

The intensity of a sound wave is the amount of energy that passes through a unit area in a specific direction per unit time. It is measured in watts per square meter (W/m²). In simpler terms, it is the loudness or strength of a sound wave.

2. How is the intensity of a sound wave related to its amplitude?

The intensity of a sound wave is directly proportional to its amplitude. This means that as the amplitude of a sound wave increases, the intensity also increases. In other words, the louder a sound is, the higher its intensity will be.

3. How is the intensity of a sound wave affected by distance?

The intensity of a sound wave decreases as the distance from the source increases. This is because the energy from the sound wave spreads out as it travels, resulting in a decrease in intensity. The relationship between intensity and distance follows the inverse square law, which means that the intensity decreases by the square of the distance from the source.

4. What is the unit of measurement for intensity in sound waves?

The unit of measurement for intensity in sound waves is watts per square meter (W/m²). It can also be measured in decibels (dB), which is a logarithmic scale that compares the intensity of a sound wave to a reference level.

5. How does the intensity of a sound wave affect the human ear?

The intensity of a sound wave can have a significant impact on the human ear. Prolonged exposure to high intensity sounds can cause hearing damage and loss. On the other hand, low intensity sounds may not be audible to the human ear. The range of intensity that is considered safe for human hearing is between 0 and 120 decibels.

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