Question

The sound from a busy highway contains a 500 Hz Fourier component whose power at the highway is 1.5 ✕ 10⁻⁶ watt/m. (Ignore sound interactions with the ground).

(a)What are the sound intensity (in W/m²), the sound intensity level (in dB) and the loudness (in phon) of that Fourier component at a distance of 25 m from the highway?

intensity=?  W/m²

intensity level =? dB

loudness=?  phon

(b)What are the sound intensity (in W/m²), the sound intensity level (in dB) and the loudness (in phon) of that Fourier component at a distance of 50 m from the highway?

intensity=? W/m²

intensity level=? dB

loudness=? phon

Answer 1

(a) Intensity (I) will be

Reference value for intensity, I₀ = 10^-12 W/m². Therefore, the intensity level in dB will be

For a pure tone at 1 kHz, loudness in phon equals sound pressure level in decibels (dB). For pure tones at much higher or lower frequency, loudness in phon will be less than sound pressure level in dB because hearing is less sensitive as you move away from the neighborhood of 1 kHz. You can get an idea of loudness from the graph below (SPL Vs Frequency).

Sound loudness is a subjective term describing the strength of the ear's perception of a sound. It is intimately related to sound intensity but can by no means be considered identical to intensity.

(b) Intensity (I) will be

Reference value for intensity, I₀ = 10^-12 W/m². Therefore, the intensity level in dB will be

Similar explanation for the loudness calculation. It is a comparative term and does not have specific value of it.