the intensity level of a sound A is5dB greater than that of sound B and 3dB less than that of C. determine the ratio (Ic/Ib) of the intensity of sound C to that of sound B.
To determine the ratio of the intensity of sound C to that of sound B (Ic/Ib), we need to compare the intensity levels of the sounds.
First, let's assign variables to the intensity levels of each sound:
- Sound A: IA
- Sound B: IB
- Sound C: IC
We are given two pieces of information:
1. The intensity level of sound A is 5dB greater than that of sound B: IA = IB + 5dB.
2. The intensity level of sound A is 3dB less than that of sound C: IA = IC - 3dB.
Now, let's solve these equations to find the values of IA, IB, and IC:
From equation 1, IA = IB + 5dB (eq. 1)
From equation 2, IA = IC - 3dB (eq. 2)
Since both equations equal IA, we can set them equal to each other:
IB + 5dB = IC - 3dB
Next, we'll isolate IC on one side by subtracting IB from both sides:
IC = IB + 5dB + 3dB
IC = IB + 8dB
Finally, we have the ratio Ic/Ib:
(Ic/Ib) = IC/IB
Substituting the value of IC into the equation:
(Ic/Ib) = (IB + 8dB)/IB
Simplifying the expression, we get the final answer:
(Ic/Ib) = 1 + (8dB/IB)
Therefore, the ratio of the intensity of sound C to that of sound B (Ic/Ib) is 1 + (8dB/IB).