A 60 dB sound wave strikes an eardrum whose area is 4.1×10^−5 m^2.
How much energy is absorbed by the eardrum per second?
At this rate, how long would it take your eardrum to receive a total energy of 4.6 J?
Convert 60 dB to sound power intensity in W/m^2.
For help doing this, see
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/intens.html
Then multiply that by the eardrum area fr power level absorbed.
4.6/(sound intensity) = time for 4.6 Joules to be received.
To find the amount of energy absorbed by the eardrum per second, we can use the formula:
Energy = Power × Time
We know that the power is equal to the intensity multiplied by the area:
Power = Intensity × Area
The intensity can be calculated using the formula:
Intensity = (Sound level in dB - Reference level) / 10
The reference level for intensity is 10^(-12) W/m^2.
Let's calculate the intensity:
Intensity = (60 dB - 0 dB) / 10 = 6
Now we can calculate the power:
Power = Intensity × Area = 6 W/m^2 × 4.1×10^(-5) m^2 = 2.46×10^(-4) W
Next, we can calculate the time it takes for the eardrum to receive a total energy of 4.6 J using the formula:
Time = Energy / Power
Time = 4.6 J / 2.46×10^(-4) W = 1.87 × 10^4 seconds
Therefore, the amount of energy absorbed by the eardrum per second is 2.46×10^(-4) W, and it would take approximately 18,700 seconds for the eardrum to receive a total energy of 4.6 J.
To determine the amount of energy absorbed by the eardrum per second, we first need to calculate the intensity of the sound wave using the formula:
Intensity = (Power) / (Area)
Given that the sound wave has a decibel level of 60 dB, we can convert this to intensity using the formula:
Intensity (in watts/m^2) = 10^((dB - 12) / 10)
Plugging in the values:
Intensity = 10^((60 - 12) / 10) = 10^(48/10) = 10^4.8 ≈ 6309.57 W/m^2
Now, we can find the energy absorbed by the eardrum per second using the formula:
Energy absorbed per second = Intensity * Area
Plugging in the values:
Energy absorbed per second = 6309.57 W/m^2 * (4.1×10^−5 m^2) ≈ 0.258 J/s
Therefore, the eardrum absorbs approximately 0.258 J of energy per second.
To find out how long it would take for the eardrum to receive a total energy of 4.6 J, we can use the formula:
Time = Energy total / Energy absorbed per second
Plugging in the values:
Time = 4.6 J / 0.258 J/s ≈ 17.829 seconds
Therefore, it would take approximately 17.829 seconds for the eardrum to receive a total energy of 4.6 J.