Sound is detected when a sound wave causes the eardrum to vibrate. Typically, the diameter of the eardrum is about 8.4 mm in humans. How much energy is delivered to your eardrum each second when someone whispers 20dB a secret in your ear?
20dB above what? 1milliwatt , or the threshold of hearing.
I will be happy to critique your work.
I don't know...but this is what i was asked
To determine the energy delivered to the eardrum, we need to calculate the intensity of the sound wave first. The intensity (I) of a sound wave is measured in watts per square meter (W/m^2) and can be calculated using the formula:
I = P / A
Where:
- I is the intensity of the sound wave in W/m^2
- P is the power (in watts) of the sound wave
- A is the area (in square meters) over which the sound wave is spread
First, we need to convert the sound level of 20dB to an intensity level:
dB = 10 * log10 (I / I0)
Where:
- dB is the sound level in decibels
- I is the sound wave intensity
- I0 is the reference intensity (generally set at 1 x 10^-12 W/m^2)
Rearranging the equation to solve for I:
I / I0 = 10^(dB / 10)
Now plug in the values:
I / (1 x 10^-12 W/m^2) = 10^(20 / 10)
I = (1 x 10^-12 W/m^2) * 10^(20 / 10)
Next, we need to calculate the power (P) of the sound wave. Power is given by the equation:
P = I * A
Given that the diameter of the eardrum is 8.4 mm, we can calculate the area (A) using the formula:
A = π * r^2
Where:
- A is the area in square meters
- r is the radius of the eardrum
Converting the diameter to radius:
r = (8.4 mm) / 2
r = 4.2 mm = 0.0042 m
Now we can calculate the area:
A = π * (0.0042 m)^2
Finally, we can calculate the power (P) using the intensity (I) and the area (A):
P = I * A
Substituting the values:
P = [(1 x 10^-12 W/m^2) * 10^(20 / 10)] * [π * (0.0042 m)^2]
Evaluating the equation will give you the power delivered to the eardrum each second when someone whispers a 20dB secret in your ear.
To calculate the energy delivered to your eardrum each second when someone whispers a secret in your ear, we can use the concept of sound intensity. Sound intensity measures the power of sound waves.
First, let's convert the sound level of 20 dB to sound intensity. Sound intensity is measured on a logarithmic scale called the decibel (dB), which compares the power of a sound wave to a reference value. The formula to convert sound level to sound intensity is:
I = Io * 10^(L/10)
Where I is the sound intensity, Io is the reference intensity (usually taken as 10^-12 W/m^2), and L is the sound level in dB.
Substituting the given values:
L = 20 dB
Io = 10^-12 W/m^2
I = (10^-12) * 10^(20/10)
I = (10^-12) * 10^2
I = (10^-12) * 100
I = 10^-10 W/m^2
Now, to calculate the energy delivered to your eardrum each second, we need to multiply the sound intensity by the area of your eardrum. The formula for energy is:
Energy = Intensity * Area
The area of a circle can be calculated using the formula:
Area = pi * (radius)^2
Given that the diameter of the eardrum is about 8.4 mm, we can calculate the radius by dividing it by 2:
Radius = 8.4 mm / 2 = 4.2 mm = 0.0042 m
Now we can calculate the area of the eardrum:
Area = pi * (0.0042)^2 = pi * 0.0042^2 ≈ 5.59 * 10^-5 m^2
Finally, we can calculate the energy delivered to the eardrum each second:
Energy = Intensity * Area = 10^-10 W/m^2 * 5.59 * 10^-5 m^2 = 5.59 * 10^-15 W
So, approximately 5.59 * 10^-15 Watts of energy is delivered to your eardrum each second when someone whispers a secret in your ear at 20 dB.