Final answer:
The intensity of the sound wave can be calculated using the given pressure amplitude and the temperature of the air. By using the formulas for density and velocity, we can determine the intensity of the sound wave to be approximately 1.25 W/m².
Step-by-step explanation:
The intensity of a sound wave can be calculated using the formula:
I = (Ap)² / (2ρv)
where I is the intensity of the sound wave, Ap is the pressure amplitude, ρ is the density of the medium, and v is the velocity of the sound wave.
In this case, we are given the pressure amplitude (Ap = 0.5 Pa) and the temperature of the air (20ºC).
The density of air at 20ºC can be calculated using the ideal gas law:
ρ = (P₀ / (R * T₀)) * (T + 273.15)
where P₀ is the atmospheric pressure, R is the ideal gas constant, T₀ is the standard temperature (273.15 K), and T is the temperature in Celsius.
The velocity of sound in air at 20ºC can be calculated using the formula:
v = √(γ * R * T)
where γ is the adiabatic index for air (approximately 1.4).
By plugging in the values and calculating, we find that the intensity of the sound wave is approximately 1.25 W/m².