You are trying to overhear a juicy conversation, but from your distance of 16.0 , it sounds like only an average whisper of 20.0 . So you decide to move closer to give the conversation a sound level of 65.0 instead.
How close should you come?
Your school subject is NOT college.
You need to include the dimensions of the numbers you are quoting. Is the distance in meters? Is the sound level in decibels? Whatever it is, say so.
A 45 dB increase in sound level is a factor of
10^4.5 = 31,620
increase in sound power per area.
Use the inverse square law to see how close you have to get
To calculate how close you should come to achieve the desired sound level, you can use the inverse square law formula for sound intensity:
I2 = I1 * (r1 / r2)^2
Where:
I1 = initial sound intensity (20.0)
I2 = desired sound intensity (65.0)
r1 = initial distance from the conversation (16.0)
r2 = desired distance from the conversation (unknown)
Rearranging the formula to solve for r2, we have:
r2 = sqrt((I1 * r1^2) / I2)
Plugging in the values we know:
r2 = sqrt((20.0 * 16.0^2) / 65.0)
r2 ≈ 16.036
Therefore, to achieve a sound level of 65.0 , you should move approximately 16.036 units closer to the conversation.
To determine how close you should come to achieve a sound level of 65.0, we can use the inverse square law of sound propagation:
L2 = L1 + 20 * log10(d2/d1)
Where:
L1 is the initial sound level (20.0 in this case),
L2 is the desired sound level (65.0),
d1 is the initial distance (16.0),
d2 is the unknown distance we need to find.
Let's solve this equation for d2:
65 = 20 * log10(d2/16.0)
log10(d2/16.0) = 65/20
log10(d2/16.0) = 3.25
Now we need to convert the logarithmic equation into an exponential one:
10^(log10(d2/16.0)) = 10^3.25
d2/16.0 = 10^3.25
d2 = 16.0 * 10^3.25
Using a calculator, we find:
d2 ≈ 1,586.33
Therefore, to achieve a sound level of 65.0, you should move approximately 1,586.33 units closer to the conversation. The specific unit of distance is not mentioned, so it depends on the context.