A microphone has an area of 3.8 cm2. It receives during a 2.87 s time period a sound energy of 4.2x10-11 J. What is the intensity of the sound?
To find the intensity of the sound, you can use the formula:
Intensity = Energy / Time / Area
Given:
Energy = 4.2 × 10^(-11) J
Time = 2.87 s
Area = 3.8 cm^2
First, convert the area from cm^2 to m^2:
Area = 3.8 cm^2 = 3.8 × 10^(-4) m^2
Now, substitute the values into the formula:
Intensity = (4.2 × 10^(-11) J) / (2.87 s) / (3.8 × 10^(-4) m^2)
Next, divide the energy by the time and area:
Intensity = (4.2 × 10^(-11) J) / (2.87 s) / (3.8 × 10^(-4) m^2)
= (4.2 × 10^(-11) J) / (2.87 s × 3.8 × 10^(-4) m^2)
= 4.2 × 10^(-11) J / (1.0936 × 10^(-3) s⋅m^2)
= 3.84 × 10^(-8) J⋅s^(-1)⋅m^(-2)
Therefore, the intensity of the sound is approximately 3.84 × 10^(-8) J⋅s^(-1)⋅m^(-2).