Question

calculate the change in sound level when the intensity of a sound is doubled

Answer 1

QUESTION: Calculate the change in sound level when the intensity of a sound is doubled

SOLUTION:

As in the task it is not specified whether to calculate the change in sound intensity level or sound pressure level, let's calculate the change in sound intensity level.

$$\mathrm {L} _ {1} = 1 0 \lg \frac {\mathrm {I} _ {1}}{\mathrm {I} _ {0}} \rightarrow \text {IS THE GENERAL FORMULA}$$ $$\mathrm {L} _ {2} = 1 0 \lg \frac {\mathrm {I} _ {2}}{\mathrm {I} _ {0}}$$ $$\mathrm {As} \quad \mathrm {I} _ {2} = 2 \mathrm {I} _ {1}$$ $$\mathrm {L} _ {2} - \mathrm {L} _ {1} = 1 0 \lg \frac {2 \mathrm {I} _ {1}}{\mathrm {I} _ {0}} - 1 0 \lg \frac {\mathrm {I} _ {1}}{\mathrm {I} _ {0}} = 1 0 \lg \left(\frac {2 \mathrm {I} _ {1}}{\mathrm {I} _ {0}} \cdot \frac {\mathrm {I} _ {0}}{\mathrm {I} _ {1}}\right) = 1 0 \lg 2 = 3. 0 3 \mathrm {dB}$$

ANSWER:

$$\mathrm {L} _ {2} - \mathrm {L} _ {1} = 3. 0 3 \mathrm {dB}$$