Expensive amplifier A is rated at 210W , while the more modest amplifier B is rated at 45W .
Estimate the sound level in decibels you would expect at a point 9.0m from a loudspeaker connected in turn to each amp.
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To estimate the sound level in decibels (dB) at a point 9.0m from the loudspeaker connected to each amplifier, you need to consider the power output of the amplifiers and the distance from the loudspeaker.
The sound level in decibels can be calculated using the formula:
L = 10 * log10(I/I0)
Where:
L is the sound level in decibels,
I is the intensity of the sound, and
I0 is the reference intensity.
In this case, we need to determine the intensity of the sound produced by each amplifier at a point 9.0m away.
First, let's calculate the intensity for amplifier A with a power rating of 210W:
The intensity of sound decreases with distance according to the inverse-square law. The formula for intensity is:
I = P / (4 * π * r^2)
Where:
I is the intensity of the sound,
P is the power output of the amplifier, and
r is the distance from the source.
Substituting the values:
I_A = 210W / (4 * π * (9.0m)^2)
Next, let's calculate the intensity for amplifier B with a power rating of 45W:
I_B = 45W / (4 * π * (9.0m)^2)
Now that we have the intensities for both amplifiers, we can calculate the sound levels in decibels:
L_A = 10 * log10(I_A/I0)
L_B = 10 * log10(I_B/I0)
Note: In order to complete the calculation, we would need the reference intensity, I0. The reference intensity is the lowest intensity that the average human ear can hear, which is usually set at 1 x 10^-12 W/m^2.
Unfortunately, we don't have the reference intensity value in this case, so we cannot provide an accurate estimation of the sound levels in decibels.