Sound and decibels at distance

174 Views Asked by At

If I have an object that is 53 decibels at x distance, how many decibels would y objects be at the same distance x, assuming they all created 53 decibels.

1

There are 1 best solutions below

0
On

The "bel" is a logarithmic unit. Every increase of one bel is an tenfold increase in sound intensity. A decibel is one tenth of a bel.

Since our original object is at $53$ dB, which is $5.3$ B, we need to measure how many times the intensity has increased. Clearly, the intensity increases by a factor of $y$.

So the increase in bels is $\log_{10} y$. Hence, the collection of $y$ objects has intensity of $53 + 10 \log_{10} y$ dB.