Problem #12: The Intensity Of Sound Wave A Is 100 Times That Of Sound Wave B. Relative To Wave B, The Sound Level Of Wave A Is:A. -2 DB B. +2 DB C. +10 DB D. +20 DB E. +100 DB

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Understanding the Basics of Sound Intensity

In physics, sound intensity is a measure of the power per unit area carried by a sound wave. It is an essential concept in understanding how sound behaves and interacts with its environment. In this problem, we are given two sound waves, A and B, with different intensities. We need to determine the relative sound level of wave A compared to wave B.

The Formula for Sound Level

The sound level, also known as the decibel (dB) level, is a logarithmic measure of the intensity of a sound wave. It is calculated using the formula:

dB = 10 log(I/I0)

where I is the intensity of the sound wave, and I0 is a reference intensity, typically 10^-12 W/m^2.

The Intensity of Sound Waves A and B

We are given that the intensity of sound wave A is 100 times that of sound wave B. Mathematically, this can be expressed as:

I_A = 100 * I_B

where I_A is the intensity of sound wave A, and I_B is the intensity of sound wave B.

Calculating the Sound Level of Wave A Relative to Wave B

To calculate the sound level of wave A relative to wave B, we need to use the formula for sound level and substitute the given intensities.

dB = 10 log(I_A/I_B)

Since I_A = 100 * I_B, we can substitute this into the formula:

dB = 10 log(100 * I_B/I_B)

Simplifying the expression, we get:

dB = 10 log(100)

Using a calculator or a logarithmic table, we find that:

log(100) = 2

Therefore, the sound level of wave A relative to wave B is:

dB = 10 * 2 = 20 dB

Conclusion

In conclusion, the sound level of wave A relative to wave B is +20 dB. This means that wave A is 100 times more intense than wave B, and its sound level is 20 dB higher than that of wave B.

Answer

The correct answer is D. +20 dB.

Additional Information

To further understand the concept of sound intensity and sound level, let's consider a few more examples.

  • If the intensity of sound wave A is 10 times that of sound wave B, what is the relative sound level of wave A compared to wave B?
  • If the intensity of sound wave A is 1000 times that of sound wave B, what is the relative sound level of wave A compared to wave B?

Using the same formula and calculations as before, we can determine the relative sound levels in these cases.

  • For a 10-fold increase in intensity, the relative sound level is +10 dB.
  • For a 1000-fold increase in intensity, the relative sound level is +30 dB.

These examples illustrate the logarithmic nature of sound level and how it relates to the intensity of a sound wave.

Key Takeaways

  • The sound level of a sound wave is a logarithmic measure of its intensity.
  • The formula for sound level is dB = 10 log(I/I0), where I is the intensity of the sound wave, and I0 is a reference intensity.
  • The relative sound level of two sound waves can be calculated using the formula dB = 10 log(I_A/I_B), where I_A is the intensity of sound wave A, and I_B is the intensity of sound wave B.
  • A 100-fold increase in intensity corresponds to a +20 dB increase in sound level.
    Problem #12: The Intensity of Sound Waves - Q&A =====================================================

Understanding the Basics of Sound Intensity

In physics, sound intensity is a measure of the power per unit area carried by a sound wave. It is an essential concept in understanding how sound behaves and interacts with its environment. In this problem, we are given two sound waves, A and B, with different intensities. We need to determine the relative sound level of wave A compared to wave B.

Q&A Session

Q: What is the formula for sound level?

A: The formula for sound level is dB = 10 log(I/I0), where I is the intensity of the sound wave, and I0 is a reference intensity, typically 10^-12 W/m^2.

Q: How is the relative sound level of two sound waves calculated?

A: The relative sound level of two sound waves can be calculated using the formula dB = 10 log(I_A/I_B), where I_A is the intensity of sound wave A, and I_B is the intensity of sound wave B.

Q: What is the relationship between sound intensity and sound level?

A: The sound level of a sound wave is a logarithmic measure of its intensity. This means that a small increase in intensity corresponds to a large increase in sound level.

Q: How does the sound level of a sound wave change when its intensity is increased by a factor of 10?

A: When the intensity of a sound wave is increased by a factor of 10, its sound level increases by 10 dB.

Q: How does the sound level of a sound wave change when its intensity is increased by a factor of 100?

A: When the intensity of a sound wave is increased by a factor of 100, its sound level increases by 20 dB.

Q: What is the sound level of a sound wave that is 1000 times more intense than another sound wave?

A: The sound level of a sound wave that is 1000 times more intense than another sound wave is 30 dB higher than the sound level of the less intense sound wave.

Q: How does the sound level of a sound wave change when its intensity is decreased by a factor of 10?

A: When the intensity of a sound wave is decreased by a factor of 10, its sound level decreases by 10 dB.

Q: How does the sound level of a sound wave change when its intensity is decreased by a factor of 100?

A: When the intensity of a sound wave is decreased by a factor of 100, its sound level decreases by 20 dB.

Q: What is the relationship between the sound level of two sound waves and their intensities?

A: The sound level of two sound waves is directly proportional to the logarithm of their intensities.

Key Takeaways

  • The sound level of a sound wave is a logarithmic measure of its intensity.
  • The formula for sound level is dB = 10 log(I/I0), where I is the intensity of the sound wave, and I0 is a reference intensity.
  • The relative sound level of two sound waves can be calculated using the formula dB = 10 log(I_A/I_B), where I_A is the intensity of sound wave A, and I_B is the intensity of sound wave B.
  • A small increase in intensity corresponds to a large increase in sound level.
  • The sound level of a sound wave changes logarithmically with its intensity.

Conclusion

In conclusion, the sound level of a sound wave is a logarithmic measure of its intensity. The formula for sound level is dB = 10 log(I/I0), and the relative sound level of two sound waves can be calculated using the formula dB = 10 log(I_A/I_B). A small increase in intensity corresponds to a large increase in sound level, and the sound level of a sound wave changes logarithmically with its intensity.