Question

Review Conceptual Example 8 as background for this problem. A loudspeaker is generating sound in a room. At a certain point, the sound waves coming directly from the speaker (without reflecting from the walls) create an intensity level of 75.0 dB. The waves reflected from the walls create, by themselves, an intensity level of 72.0 dB at the same point. What is the total intensity level?

Answer 1

Level = 76.8 dB

Step-by-step explanation:

Level of sound intensity is related to the intensity of sound by the following formula

`L = 10 Log (I)/(I_0)`

so from above formula we can find the intensity of sound for 75 dB

`75.0 dB = 10 Log(I_1)/(10^(-12))`

`I_1 = 3.16 * 10^(-5) W/m^2`

now for another sound level of 72.0 dB we have

`72 = 10 Log(I_2)/(10^(-12))`

so we have

`I_2 = 1.58 * 10^(-5) W/m^2`

now the total intensity due to both sounds

`I = I_1 + I_2`

`I = 3.16 * 10^(-5) + 1.58 * 10^(-5)`

`I = 4.74 * 10^(-5) W/m^2`

Now the level of resultant sound is

`L = 10 Log(4.74 * 10^(-5))/(10^(-12))`

`L = 76.8 dB`