A constant tone is being applied to a speaker. The voltage across the speaker is 5 volts. The voltage across the speaker is increased to 15 volts in order to increase the sound level. What is the decibel gain, rounded to the nearest decibel?
10 log (15/5)^2
To calculate the decibel gain, we can use the formula:
dB gain = 10 * log10(V2/V1)
Where:
V1 = initial voltage across the speaker (5 volts)
V2 = final voltage across the speaker (15 volts)
Let's substitute the values into the formula and calculate the decibel gain:
dB gain = 10 * log10(15/5)
= 10 * log10(3)
≈ 10 * 0.4771
≈ 4.771
Rounded to the nearest decibel, the decibel gain is approximately 4.8 decibels.
To calculate the decibel gain, we need to use the formula:
Gain (in decibels) = 10 * log10 (P2 / P1)
where P1 is the initial power and P2 is the final power.
Since we are given the voltage across the speaker, we need to convert it to power. Power (P) is related to voltage (V) by the formula:
P = (V^2) / R
where R is the speaker's impedance, which we don't have information about. However, since we are told that the voltage remains constant and only the sound level is increased, we can assume that the impedance of the speaker remains constant as well. Therefore, we can ignore the impedance when comparing the initial and final powers.
Let's calculate the initial and final powers:
Initial Power (P1) = (5^2) = 25
Final Power (P2) = (15^2) = 225
Now we can substitute these values into the formula to find the decibel gain:
Gain (in decibels) = 10 * log10 (225 / 25) ~= 10 * log10 (9) ~= 10 * 0.9542 ~= 9.542
Rounded to the nearest decibel, the decibel gain is approximately 9.5 decibels.