To find the intensity of sound, we can use the formula:
Intensity = Energy / Time
The given energy is 1.0x10^-11 J, and the time is 6.00 s. Plugging in these values:
Intensity = (1.0x10^-11 J) / (6.00 s)
Intensity ≈ 1.67x10^-12 W/m^2
Therefore, the intensity of the sound is approximately 1.67x10^-12 W/m^2.
Now, let's move on to the second part of your question. To find the variation of pressure in the sound wave, we can use the formula:
Intensity = (Density) x (Speed of Sound)^2 x (Amplitude)^2
Here, we need to solve for the amplitude (A), which represents the variation of pressure. Rearranging the equation:
(Amplitude)^2 = Intensity / [(Density) x (Speed of Sound)^2]
The given values are:
Intensity = 1.67x10^-12 W/m^2
Density of air = 1.2 kg/m^3
Speed of sound = 343 m/s
Plugging in these values:
(Amplitude)^2 = (1.67x10^-12 W/m^2) / [(1.2 kg/m^3) x (343 m/s)^2]
Calculating the right-hand side of the equation and taking the square root of the result will give us the amplitude.
(Amplitude) ≈ √[(1.67x10^-12) / (1.2 x 343^2)]
(Amplitude) ≈ 2.69x10^-5 N/m^2
Therefore, the variation of pressure in the sound wave is approximately 2.69x10^-5 N/m^2.