Hi I am absolutely stumped on this question.
A loudspeaker is placed between two observers who are 110 m apart, along the line connecting them. If one observer records a sound level of 60.1 dB and the other records a sound level of 74.9 dB, how far is the speaker from each observer?
What I did for this is
I found the the Intensities of both the sound levels.
Then using the formula r1= SQRT(I2/I1)*R2
I would solve for r1 and then do r1+r2=113 to find r2.
I also don't know what value to assign for I2 and I1, i tried both ways but its wrong.
Please Help!
Thanks In Advance
This is the third post of this question. Please try to find my previous answer
To solve this problem, you are on the right track with the formula r1 = √(I2/I1) * r2. However, you need to assign the correct values for I2 and I1.
Intensity (I) is related to sound level (L) by the formula:
I = 10^(L/10)
Given that the first observer records a sound level of 60.1 dB, you can calculate the intensity as:
I1 = 10^(60.1/10)
Similarly, for the second observer with a sound level of 74.9 dB, the intensity is:
I2 = 10^(74.9/10)
Now you have the correct values for I2 and I1.
To find r1, substitute the values into the formula:
r1 = √(I2/I1) * r2
r1 = √(I2/I1) * 110
Next, solve for r1 by substituting the values of I2, I1, and r2 into the equation.
Finally, to find r2, you can use the relationship r1 + r2 = 110 since the observers are 110 m apart.
Substitute the value of r1 you calculated into r1 + r2 = 110, and solve for r2.
I hope this helps! Let me know if you have any additional questions.