Question

Sound waves at ultrasonic frequencies attenuate much faster than audible sound waves. The sound intensity level of a point source of ultrasonic sound waves is measured as 100 dB at a distance of 1.00 m from the source and 65 dB at 2.00 m. Assuming the waves spread in all directions, what is the attenuation coefficient alpha? [Answer in 1/m to within 5%]

Answer 1

ultrasonic sound waves is measured as 100 dB

at a distance of 1.00 m

from the source and 65 dB

at 2.00 m

using equation

= 10 log₁₀( I/I_o )

100 = 10 log₁₀( I/10^-12 )

10 = log₁₀( I/10^-12 )

I/10^-12 = 10¹⁰

I = 10¹⁰ x 10^-12

I = 10^-2 W/m²

the sound intensity level is

I = I_o exp( - x )

I / I_o = exp( - x )

= ( 1/x ) ln ( I_o / I )

= ( 1/ 2 - 1 ) ln ( 10^-12 / 10^-2 )

= ln ( 10^-12 / 10^-2 )

= 23.02 /m