# The Principle of Linear Superposition and Young's Double-Slit Experiment (1 Viewer)

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#### BoogieL80

I'm having problems with the following problem:

A rock concert is being held in an open field. Two loudspeakers are separated by 9.00 m. As an aid in arranging the seating, a test is conducted in which both speakers vibrate in phase and produce an 80.0 Hz bass tone simultaneously. The speed of sound is 343 m/s. A reference line is marked out in front of the speakers, perpendicular to the midpoint of the line between the speakers. Relative to either side of this reference line, what is the smallest angle that locates the places where destructive interference occurs? People seated in these places would have trouble hearing the 80.0 Hz bass tone.

The only thing I can figure out is that somehow, using trigonometry and the formula sin * theta = (m + 1/2 ) * wavelength/ distance I'm suppose to get my answer. But I'm a little confused how the frequency plays a role? I tried assuming that it was maybe my M value, but that didn't work. I thought that maybe it was suppose to be the "lengths" of the triangles, but that didn't work. I tried solving for m when sin * theta = 0, but that didn't work. Any help would be appreciated.

#### nrqed

Homework Helper
Gold Member
BoogieL80 said:
I'm having problems with the following problem:

A rock concert is being held in an open field. Two loudspeakers are separated by 9.00 m. As an aid in arranging the seating, a test is conducted in which both speakers vibrate in phase and produce an 80.0 Hz bass tone simultaneously. The speed of sound is 343 m/s. A reference line is marked out in front of the speakers, perpendicular to the midpoint of the line between the speakers. Relative to either side of this reference line, what is the smallest angle that locates the places where destructive interference occurs? People seated in these places would have trouble hearing the 80.0 Hz bass tone.

The only thing I can figure out is that somehow, using trigonometry and the formula sin * theta = (m + 1/2 ) * wavelength/ distance I'm suppose to get my answer. But I'm a little confused how the frequency plays a role? I tried assuming that it was maybe my M value, but that didn't work. I thought that maybe it was suppose to be the "lengths" of the triangles, but that didn't work. I tried solving for m when sin * theta = 0, but that didn't work. Any help would be appreciated.
Remember that $\lambda f = v$. using the frequency and the speed of sound gives you the wavelength.

Patrick

#### BoogieL80

Thank you. I feel like such an idiot now....

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