When the volume control on a stereo system is increased, the voltage across a loudspeaker changes from V1 to V2, and the decibel increase in gain is given by
db = 20 log [V2/V1]
Find the decibel increase if the voltage changes from 3 volts to 4.5 volts.
V1 = 3 , V2 = 4.5
V2 / V1 = 4.5 / 1.5 = 3 ∙ 1.5 / 3 = 1.5
dB = 20 ∙ log ( 1.5 )
To find the decibel increase, we can substitute the given values into the formula:
db = 20 log [V2/V1]
where V1 = 3 volts and V2 = 4.5 volts.
Substituting these values in the formula, we get:
db = 20 log [4.5/3]
To evaluate this expression, we need to calculate the ratio 4.5/3. This can be simplified as:
4.5/3 = 1.5
Now, we can substitute this value into the formula:
db = 20 log [1.5]
To find the logarithm of 1.5, we can use a calculator. Taking the log (base 10) of 1.5, we get approximately 0.176.
Substituting this value into the formula, we have:
db = 20 * 0.176
Evaluating this expression, we get:
db ≈ 3.52
Therefore, the decibel increase is approximately 3.52 dB when the voltage changes from 3 volts to 4.5 volts.