Answer:
100 times
Explanation:
The sound intensity level β of a sound with an intensity I is mathematically given as:
[tex]\beta (dB)=10log_{10}(\frac{I}{I_0} )[/tex], Where [tex]I_0[/tex] = lowest sound intensity for a normal person at a frequency of 1000 Hz
For the quiet part:
[tex]\beta_1 = 10*log_{10}*(I_1/I_0)[/tex]
For the loud part:
[tex]\beta_2 = 10*log_{10} * (I_2/I_0)[/tex]
Hence,
[tex]\beta_2 - \beta_1 = 10*log_{10} * (I_2/I_1)[/tex]
70-50 = [tex]10*log_{10} * (I_2/I_1)[/tex]
[tex]log_{10} * (I_2/I_1)[/tex] = 2
[tex](I_2/I_1)[/tex] = 100
[tex]I_2[/tex] = 100[tex]I_1[/tex]
Therefore, the latter sound ([tex]I_2[/tex]) is 100 times louder than the former sound ([tex]I_1[/tex])
