To find the intensity of the sound, we can use the formula:
Intensity = Energy / Area * Time
1) Given that the area of the microphone is 6.7 cm2 (or 6.7 * 10^-4 m^2), the time period is 4.62 s, and the sound energy is 2.5x10^-11 J, we can substitute these values into the formula:
Intensity = (2.5x10^-11 J) / (6.7x10^-4 m^2) * (4.62 s)
Simplifying this expression, we get:
Intensity = 2.5x10^-11 J / (6.7x10^-4 m^2 * 4.62 s)
Now we can do the multiplication in the denominator:
Intensity = 2.5x10^-11 J / 3.086x10^-6 m^2s
Dividing the two values, we get:
Intensity = 8.11x10^-6 W/m^2
Therefore, the intensity of the sound is 8.11x10^-6 W/m^2.
2) To find the variation of pressure in the sound wave, we can use the formula:
Pressure = √(2 * Intensity * Density * Speed of Sound)
Given that the intensity is 8.11x10^-6 W/m^2, the density of air is 1.2 kg/m^3, and the speed of sound is 343 m/s, we can substitute these values into the formula:
Pressure = √(2 * (8.11x10^-6 W/m^2) * (1.2 kg/m^3) * (343 m/s))
Simplifying this expression, we get:
Pressure = √(2 * 8.11x10^-6 W/m^2 * 1.2 kg/m^3 * 343 m/s)
Now we can do the multiplication inside the square root:
Pressure = √(2 * 8.11x10^-6 W/m^2 * 1.2 kg/m^3 * 343 m/s)
Pressure = √(1.0108x10^-2 N/m^2)
Taking the square root of 1.0108x10^-2, we get:
Pressure = 0.1005 N/m^2
Therefore, the variation of pressure in the sound wave is 0.1005 N/m^2.