Answer:
[tex]4.90167\times 10^{-17}\ J[/tex]
Explanation:
I = Hearing intensity = [tex]1\times 10^{-12}\ W/m^2[/tex]
A = Area = [tex]\pi r^2[/tex]
d = Diameter = 7.9 mm
r = Radius = [tex]\dfrac{d}{2}=\dfrac{7.9}{2}=3.95\ mm[/tex]
Power is given by
[tex]P=IA\\\Rightarrow P=1\times 10^{-12}\times \pi \times (3.95\times 10^{-3})^2\\\Rightarrow P=4.90167\times 10^{-17}\ W[/tex]
t = Time the eardrum is exposed to sound = 1 second
Energy is given by
[tex]E=Pt\\\Rightarrow E=4.90167\times 10^{-17}\times 1\\\Rightarrow E=4.90167\times 10^{-17}\ J[/tex]
The energy transferred to the eardrum is [tex]4.90167\times 10^{-17}\ J[/tex]
Answer:
The sound energy is [tex]5\times10^{-5}\ J[/tex].
Explanation:
Given that,
Diameter = 7.90 mm
Suppose the intensity for threshold of pain is 1.00 W/m².
We need to calculate the area
Formula of area
[tex]A=\pi r^2[/tex]
Put the value into the formula
[tex]A=\pi\times(\dfrac{7.90\times10^{-3}}{2})^2[/tex]
[tex]A=0.000049[/tex]
[tex]A=4.9\times10^{-5}\ m^2[/tex]
[tex]A=5\times10^{-5}\ m^2[/tex]
We need to calculate the power
Using formula of power
[tex]P=IA[/tex]
Where, P = Power
I = intensity
A = area
Put the value into the formula
[tex]P=1.00\times10^{-12}\times5\times10^{-5}[/tex]
[tex]P=5\times10^{-17}\ W[/tex]
We need to calculate the incident power at the threshold of pain
Using formula of power
[tex]P=IA[/tex]
[tex]P=1.00\times5\times10^{-5}[/tex]
[tex]P=5\times10^{-5}\ W[/tex]
We need to calculate the energy
Using formula of energy
[tex]E=Pt[/tex]
Where. P = power
t = time
Put the value into the formula
[tex]E=5\times10^{-5}\times1[/tex]
[tex]E=5\times10^{-5}\ J[/tex]
Hence, The sound energy is [tex]5\times10^{-5}\ J[/tex].
