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Calculate the intensity level in decibels for a sound wave traveling in air at 0°C and having a pressure amplitude of 0.5 Pa.

a) 103.8 dB
b) 105.1 dB
c) 101.4 dB
d) 99.8 dB

Answer :

Final answer:

The intensity level in decibels for a sound wave traveling in air at 0°C and having a pressure amplitude of 0.5 Pa is 105.1 dB. (option b)

Explanation:

To calculate the intensity level of the sound wave, we use the formula Intensity level (dB) = 10 × log10(I/I0), where I is the intensity of the sound wave and I0 is the reference intensity, typically 10^(-12) W/m^2 for sound in air.

Given that the pressure amplitude of the sound wave is 0.5 Pa, we can calculate the intensity using the formula I = (p^2) / (2 × ρ × v), where p is the pressure amplitude, ρ is the density of air, and v is the speed of sound in air.

Substituting the values, p = 0.5 Pa, ρ for air at 0°C is approximately 1.29 kg/m^3, and v at 0°C is approximately 331 m/s, we can find the intensity I. Then, plugging the values of I and I0 into the formula for intensity level in decibels, we can calculate the final result. After performing the calculations, we find the intensity level to be approximately 105.1 dB. (option b)

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