Question

The sound from a trumpet radiates uniformly in all directions in air with a temperature of 20∘C . At a distance of 4.98 m from the trumpet the sound intensity level is 56.0 dB . The frequency is 581 Hz . Use 344 m/s for the speed of sound in air, 1.20 kg/m3 for the density of air, and 1.00×10⁻¹² W/m² for the reference intensity.

At what distance is the sound intensity level 29.0 dBdB?

Answer 1

To find the distance at which the sound intensity level is 29.0 dB, we can use the inverse square law formula for sound intensity. The inverse square law states that the intensity of sound decreases as the square of the distance increases. Using this formula, the distance is calculated to be approximately 8.75 m.

Step-by-step explanation:

To find the distance at which the sound intensity level is 29.0 dB, we can use the inverse square law formula for sound intensity. The inverse square law states that the intensity of sound decreases as the square of the distance increases. We can rearrange the formula to solve for the distance:

I1/I2 = (r2/r1)2

where I1 is the initial intensity level, I2 is the final intensity level, r1 is the initial distance, and r2 is the final distance. Using the given information, we can plug in the values:

56.0 dB/29.0 dB = (4.98 m/r2)2

Solving for r2, the final distance:

r2 = 4.98 m * sqrt((1056.0 dB/29.0 dB))

Calculating this value gives us a final distance of approximately 8.75 m.