Waves: Calculate the sound intensity from two speakers

[Karl Karlsson]

Homework Statement

Two similar speakers are connected to a stereo system that emits a signal of frequency 𝑓. However, the signal to speaker B is inverted so that positive voltage becomes negative (but with the same absolute value) and vice versa for negative voltages that become positive. A sound intensity meter shows 80.0 dB at a distance of 1.0 m in front of each of the speakers when only that speaker is turned on. How large will the sound intensity level of the audience be when both speakers are turned on? The sound speed is 340 m / s.

Relevant Equations

B=10lg(I/10^-12)

Two similar speakers are connected to a stereo system that emits a signal of frequency 𝑓. However, the signal to speaker B is inverted so that positive voltage becomes negative (but with the same absolute value) and vice versa for negative voltages that become positive. A sound intensity meter shows 80.0 dB at a distance of 1.0 m in front of each of the speakers when only that speaker is turned on. How large will the sound intensity level of the audience be when both speakers are turned on? The sound speed is 340 m / s.

The images below contains a picture of the problem, some values and my try of the problem. Is my solution correct? If not then why?

 

[TSny]

Your work looks good to me overall except near the end. Did you take into account that $I$ is proportional to the square of $A$ when writing the equation at the bottom of the third image?

 

[Karl Karlsson]

Your work looks good to me overall except near the end. Did you take into account that $I$ is proportional to the square of $A$ when writing the equation at the bottom of the third image?

Oh, wow. Silly me, I even wrote that the intensity was proportional to the square of the amplitude above on that same page. Thanks! I looked through it again now and I can't find anything else that is wrong either.

 

[TSny]

Everything else looks good to me.