If you increase the acoustic intensity by 1000 times, how many decibels have you gained?

If you increase the acoustic intensity by 1000 times, how many decibels have you gained?

• A. 10 db
• B. 20 db
• C. 30 db
• D. 40 db

Answer: (C)

When discussing changes in acoustic intensity measured in decibels (dB), it's important to remember that the decibel scale is logarithmic. Specifically, an increase of 10 decibels represents a tenfold increase in intensity. To determine how many decibels correspond to an increase in intensity by 1000 times, we can use the formula for calculating decibels based on intensity: \[ \text{dB} = 10 \log_{10}\left(\frac{I_2}{I_1}\right) \] where \( I_2 \) is the final intensity and \( I_1 \) is the initial intensity. In this scenario, if you increase the intensity by 1000 times, the ratio \( \frac{I_2}{I_1} \) equals 1000. Calculating the decibel increase: \[ \text{dB} = 10 \log_{10}(1000) \] \[ \text{dB} = 10 \log_{10}(10^3) \] \[ \text{dB} = 10 \times 3 \] \[ \text{dB} = 30 \] Thus,

When discussing changes in acoustic intensity measured in decibels (dB), it's important to remember that the decibel scale is logarithmic. Specifically, an increase of 10 decibels represents a tenfold increase in intensity.

To determine how many decibels correspond to an increase in intensity by 1000 times, we can use the formula for calculating decibels based on intensity:

[ \text{dB} = 10 \log_{10}\left(\frac{I_2}{I_1}\right) ]

where ( I_2 ) is the final intensity and ( I_1 ) is the initial intensity.

In this scenario, if you increase the intensity by 1000 times, the ratio ( \frac{I_2}{I_1} ) equals 1000.

Calculating the decibel increase:

[ \text{dB} = 10 \log_{10}(1000) ]

[ \text{dB} = 10 \log_{10}(10^3) ]

[ \text{dB} = 10 \times 3 ]

[ \text{dB} = 30 ]

Thus,