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Shalnov [3]
2 years ago
6

A particular person's eardrum is circular, with a diameter of 7.90 mm. How much sound energy (in J) is delivered to an eardrum i

n one second, at the threshold of human hearing? (The threshold of human hearing is taken to be 1.00 ✕ 10−12 W/m2.)
Physics
2 answers:
anastassius [24]2 years ago
8 0

Answer:

The sound energy is 5\times10^{-5}\ J.

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

A=\pi r^2

Put the value into the formula

A=\pi\times(\dfrac{7.90\times10^{-3}}{2})^2

A=0.000049

A=4.9\times10^{-5}\ m^2

A=5\times10^{-5}\ m^2

We need to calculate the power

Using formula of power

P=IA

Where, P = Power

I = intensity

A = area

Put the value into the formula

P=1.00\times10^{-12}\times5\times10^{-5}

P=5\times10^{-17}\ W

We need to calculate the incident power at the threshold of pain

Using formula of power

P=IA

P=1.00\times5\times10^{-5}

P=5\times10^{-5}\ W

We need to calculate the energy

Using formula of energy

E=Pt

Where. P = power

t = time

Put the value into the formula

E=5\times10^{-5}\times1

E=5\times10^{-5}\ J

Hence, The sound energy is 5\times10^{-5}\ J.

antiseptic1488 [7]2 years ago
3 0

Answer:

4.90167\times 10^{-17}\ J

Explanation:

I = Hearing intensity = 1\times 10^{-12}\ W/m^2

A = Area = \pi r^2

d = Diameter = 7.9 mm

r = Radius = \dfrac{d}{2}=\dfrac{7.9}{2}=3.95\ mm

Power is given by

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

t = Time the eardrum is exposed to sound = 1 second

Energy is given by

E=Pt\\\Rightarrow E=4.90167\times 10^{-17}\times 1\\\Rightarrow E=4.90167\times 10^{-17}\ J

The energy transferred to the eardrum is 4.90167\times 10^{-17}\ J

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