suppose that the separation between speakers A and B is 5.80 m and the speakers are vibrating in phase. They are playing identical 135 Hz tones, and the speed of sound is 343 m/s. What is the largest possible distance between speaker B and the observer at C, such that he observes destructive interference?
Distruive interference? Unless you put C in the line between A and B, this the asnwer is at infinity.
Now on the line between A and B, the distance from A to C has to be an odd multiple of halfwavelength greater than C to B. Now, the distance between the speakers is two wavelength. So if AC-BC is n lambda/2, then n must be one, so
AC=BC + 2.54/2 where BC= 5.8-AC
solve for AC.
Please tell me where I am going wrong.
AC = BC + 2.54/2
AC = 7.366
How come it's BC =5.8 - AC. Should it be BC= AC -5.8
because
AC = sqrt [(AB)^2 + (BC)^2]
AC = 5.8 + BC
How come it's BC =5.8 - AC? Shouldn't it be BC= AC -5.8
because
AC = sqrt [(AB)^2 + (BC)^2]
AC = 5.8 + BC
I apologize for the confusion caused by my incorrect explanation.
You are correct, it should be BC = AC - 5.8, not BC = 5.8 - AC. Thank you for bringing that to my attention.
To find the largest possible distance between speaker B and the observer at C, where destructive interference occurs, we need to find the values of AC and BC.
We have the equation AC = BC + 2.54/2, where BC = AC - 5.8.
Substituting BC = AC - 5.8 into the equation, we get:
AC = AC - 5.8 + 2.54/2
Simplifying the equation, we have:
AC = AC - 2.9 + 1.27
2.9 - 1.27 = 1.63
So, the correct value for AC is 1.63 m.
To find the largest possible distance between speaker B and the observer at C, we subtract AC from the separation between the speakers:
BC = 5.8 - AC
BC = 5.8 - 1.63
BC = 4.17 m
Therefore, the largest possible distance between speaker B and the observer at C, such that destructive interference occurs, is 4.17 m.