Question

Two sources have sound levels of 64 dB and 128 dB. What is their combined intensity? Answer in units of W/m².

a. 1.26 × 10^(6) W/m²
b. 1.58 × 10^(-6) W/m²
c. 1.99 × 10^(-6) W/m²
d. 2.51 × 10^(-6) W/m²

Answer 1

The combined intensity of the two sound sources with levels of 64 dB and 128 dB is 2.51 × 10^6 W/m².

Step-by-step explanation:

The sound levels are given in dB, which is a logarithmic scale used to measure sound intensity. To combine the sound intensities, we need to convert the dB values to actual intensities using the formula:

I = 10(L/10)

where I is the intensity in W/m² and L is the sound level in dB.

For the first source with a sound level of 64 dB:

I1 = 10(64/10) = 2511.8864 W/m²

For the second source with a sound level of 128 dB:

I2 = 10(128/10) = 25118864.318 W/m²

To find the combined intensity, we add the two intensities:

I total = I1 + I2

Itotal = 2511.8864 + 25118864.318 = 25121376.204 W/m²

Therefore, the combined intensity of the two sources is 2.51 × 106 W/m² (option d).