Why Does Destructive Interference Occur at Different Frequencies?

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Destructive interference occurs when sound waves from two speakers reach a listener at different distances, causing cancellation. In this case, the listener is 0.6m farther from one speaker, which is significant for calculating the wavelength needed for interference. The correct wavelength is twice the distance difference, resulting in a wavelength of 1.2m, not 0.12m. Using the sound velocity of 343 m/s, the lowest frequency for destructive interference is calculated to be approximately 286.25 Hz. Careful attention to detail is crucial in these calculations, as small errors can lead to incorrect results.
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Destructive Interference: Please Help!

Two loudspeakers are 2.36m apart. A person stands 2.8m from one speaker and 3.4m from the other. What is the lowest frequency at which destructive interference will occur at this point?

My answer is wrong, but this is what I did:
3.4m-2.8m=0.6m, so the person is .6m farther from one speaker than the other.
In order to sense destructive Interference, the person, must be one-half wavelength closer to or farther from one speaker than the other, the wavelength must be twice the distance difference. Therefore, Wavelength=0.12m
Using the equation Wavelength =velocity/frequency, I solved for frequency. (velocity of sound is 343 m/s).
My answer: 2858.33Hz

PLease help! Thanks!
 
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What's 2 times 0.6? :wink:
 
Haha, thanks! Those careless mistakes make such a difference!
 

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