How Does Destructive Interference Occur With Different Sound Wavelengths?

AI Thread Summary
Destructive interference occurs when sound waves from two speakers cancel each other out due to phase differences. In this scenario, one speaker emits sound with a wavelength of 0.02 m and the other with 0.05 m, separated by 3 m. The equation d sin(theta) = m(wavelength) can be applied, but it requires careful consideration of both wavelengths. To find where destructive interference first occurs along the x-axis, the phase difference created by the distance and wavelengths must be calculated. Understanding how to apply the equation with two different wavelengths is crucial for solving the problem.
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Homework Statement


Two speakers, one directly behind the other and along the x-axis, emit sound waves along the x-axis. The speaker in the back emits sound with a wavelength of .02 m and the speaker in the front emits waves with a wavelength of .05m. If the two speakers are separated by 3 m, where along the x-axis will destructive interference first occur?

Homework Equations


d sin(theta) = m(wavelength)

The Attempt at a Solution


How do I use the above equation if there are two wavelengths that I need to use?
 
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Am I using the correct equation?
 

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