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 of a sound wave is measured in decibels (dB) and is calculated using the following formula:

β = 10 log(I/I0)

where β is the sound level in decibels, I is the intensity of the sound wave, and I0 is a reference intensity.

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 Relative Sound Level

To calculate the relative sound level of wave A compared to wave B, we need to use the formula for sound level. We can substitute the given intensities into the formula:

β = 10 log(I_A/I_B) = 10 log(100 * I_B/I_B) = 10 log(100) = 10 * 2 = 20 dB

Therefore, the sound level of wave A is 20 dB higher than that of wave B.

Conclusion

In conclusion, the relative sound level of wave A compared to wave B is +20 dB. This means that wave A is 20 dB louder than wave B.

Key Takeaways

  • The intensity of sound wave A is 100 times that of sound wave B.
  • The sound level of wave A is 20 dB higher than that of wave B.
  • The formula for sound level is β = 10 log(I/I0), where β is the sound level in decibels, I is the intensity of the sound wave, and I0 is a reference intensity.

Answer

The correct answer is:

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 β = 10 log(I/I0), where β is the sound level in decibels, I is the intensity of the sound wave, and I0 is a reference intensity.

Q: How is the intensity of sound wave A related to the intensity of sound wave B?

A: The intensity of sound wave A is 100 times that of sound wave B.

Q: What is the relative sound level of wave A compared to wave B?

A: The sound level of wave A is 20 dB higher than that of wave B.

Q: Why is the sound level of wave A higher than that of wave B?

A: The sound level of wave A is higher than that of wave B because the intensity of wave A is 100 times that of wave B.

Q: What is the significance of the reference intensity (I0) in the formula for sound level?

A: The reference intensity (I0) is a standard value used to compare the intensity of different sound waves. It is typically set at 10^-12 W/m^2.

Q: Can you explain the concept of decibels (dB) in the context of sound intensity?

A: Decibels (dB) are a unit of measurement used to express the sound level of a sound wave. A higher decibel value indicates a louder sound wave.

Q: How can you use the formula for sound level to calculate the sound level of a sound wave?

A: To calculate the sound level of a sound wave, you can use the formula β = 10 log(I/I0), where β is the sound level in decibels, I is the intensity of the sound wave, and I0 is a reference intensity.

Q: What are some common applications of sound intensity in real-world scenarios?

A: Sound intensity is used in various applications, including:

  • Acoustics: to measure the sound level of a room or a sound wave
  • Noise pollution: to measure the sound level of a noise source
  • Hearing protection: to determine the sound level of a sound wave that can cause hearing damage

Conclusion

In conclusion, the relative sound level of wave A compared to wave B is +20 dB. This means that wave A is 20 dB louder than wave B. Understanding the basics of sound intensity and the formula for sound level is essential in various applications, including acoustics, noise pollution, and hearing protection.

Key Takeaways

  • The intensity of sound wave A is 100 times that of sound wave B.
  • The sound level of wave A is 20 dB higher than that of wave B.
  • The formula for sound level is β = 10 log(I/I0), where β is the sound level in decibels, I is the intensity of the sound wave, and I0 is a reference intensity.
  • Decibels (dB) are a unit of measurement used to express the sound level of a sound wave.
  • Sound intensity is used in various applications, including acoustics, noise pollution, and hearing protection.