A sound wave in air at 20० C has a frequency of 150 hz and a displacement amplitude of 5m. For this calculate pressure amplitude,intensity of sound and sound intensity level
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To calculate the pressure amplitude, intensity of sound, and sound intensity level, we need to use the formulas and equations related to sound waves. Here's how you can calculate each of them step by step:
1. Pressure Amplitude:
The pressure amplitude of a sound wave can be calculated using the formula:
Pressure Amplitude = Displacement Amplitude × ρ × c
Where:
- Displacement Amplitude is the given amplitude of 5m.
- ρ (rho) is the density of air, which is approximately 1.225 kg/m^3 at 20°C.
- c is the speed of sound in air, which is approximately 343 m/s at 20°C.
Using these values in the formula, we can calculate the pressure amplitude as follows:
Pressure Amplitude = 5m × 1.225 kg/m^3 × 343 m/s
2. Intensity of Sound:
The intensity of sound can be calculated using the formula:
Intensity = (Pressure Amplitude)^2 / (2 × ρ × c)
Using the calculated Pressure Amplitude and the given ρ and c values, we can substitute them into the formula to find the intensity.
Intensity = (Pressure Amplitude)^2 / (2 × 1.225 kg/m^3 × 343 m/s)
3. Sound Intensity Level:
The sound intensity level (SIL) is calculated using the logarithmic formula:
SIL = 10 × log10 (Intensity / I0)
Where:
- log10 is the base 10 logarithm.
- Intensity is the calculated intensity in watts per square meter (W/m^2).
- I0 is the reference intensity, which is approximately 1.0 x 10^-12 W/m^2.
Substituting the calculated intensity and the given I0 value into the formula, we can find the sound intensity level.
SIL = 10 × log10 (Intensity / (1.0 × 10^-12 W/m^2))
By following these steps and using the given values in the respective formulas, you can now calculate the pressure amplitude, intensity of sound, and sound intensity level for the given sound wave.