Question

Show that when the intensity of a sound in decibel is triples the sound intensity in watt per metre is also triples. Find this sound level

Answer 1

$$\beta = 10 \log_{10}{\frac{I}{I_0}}$$

$$3\beta = 10 \log_{10}{\frac{3I}{I_0}}$$

$$3\beta = 10 \log_{10}{\frac{3I}{I_0}}+10 \log_{10}{3}$$

$$3\beta = \beta +10 \log_{10}{3}$$

$$2\beta =10 \log_{10}{3}$$

$$\beta =5 \log_{10}{3}=2.4 \ dB$$