Find the number of decibels for the power of the sound. Round to the nearest decibel.
A rock concert, 5.3 10-6 watts/cm2
db = 10*Log(5.3*10^-6)
db = 10*(Log5.3+LOg10^-6)db = 10*(
db = 10*(0.724-6) = -53.
Correction:
db = 10*Log(5.3*10^-6)
db = 10*(Log5.3-Log10^-6)
db = 10*(0.724-6) = -53.
To find the number of decibels for the power of the sound, you can use the formula:
dB = 10 * log10(P1/P0)
where P1 is the power of the sound and P0 is the reference power.
Given that the power of the rock concert is 5.3 * 10^(-6) watts/cm^2, we need to determine the reference power.
The threshold of human hearing, also known as the reference power, is typically considered to be 10^(-12) watts/cm^2.
Substituting the values into the formula, we get:
dB = 10 * log10((5.3 * 10^(-6)) / (10^(-12)))
Simplifying this expression:
dB = 10 * log10(5.3 * 10^(-6) * 10^12)
dB = 10 * log10(5.3 * 10^6)
dB = 10 * log10(5.3) + 10 * log10(10^6)
Using a calculator, log10(5.3) ≈ 0.72428 and log10(10^6) = 6, so:
dB = 10 * 0.72428 + 10 * 6
dB ≈ 7.2428 + 60
dB ≈ 67.2428
Rounding to the nearest decibel, the number of decibels for the power of the sound at the rock concert is approximately 67 decibels.
To find the number of decibels for the power of the sound, you can use the formula:
N = 10 * log10(P/P0)
where:
N is the number of decibels,
P is the power of the sound in watts/cm2,
P0 is the reference power (usually 10-12 watts/cm2).
In this case, the power of the sound at a rock concert is given as 5.3 * 10-6 watts/cm2. Let's calculate the number of decibels:
N = 10 * log10(5.3 * 10-6 / 10-12)
First, divide the given power by the reference power:
N = 10 * log10(5.3 * 106)
Next, take the base-10 logarithm of the result:
N = 10 * log10(5.3) + 10 * log10(106)
Finally, calculate the logarithms:
N ≈ 10 * 0.72427587 + 10 * 6.02530587
N ≈ 7.2427587 + 60.2530587
N ≈ 67.4958174
Since we need to round to the nearest decibel, the number of decibels for the power of the sound at a rock concert is approximately 67 decibels.