Lowest frequency that produces an interference maximum

In summary, the problem involves finding the lowest and next lowest frequency that produces an interference maximum at a microphone's location on a line connecting two speakers. Using the equation r2 - r1 = (n-0.5)(lambda) with r2 = 2.2185 and r1 = 2.477, the value for lambda can be found and then used to solve for frequency (f = v/lambda). The value of n represents the harmonic number and must be adjusted for the lowest and next lowest frequencies.
  • #1
L1988
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Homework Statement



A microphone is located on the line connecting two speakers that are 0.517 m apart and oscillating 180° out of phase. The microphone is 1.96 m from the midpoint of the two speakers. What is the lowest frequency that produces an interference maximum at the microphone's location?

What is the next lowest frequency that produces an interference maximum at the microphone's location?



Homework Equations



r2 -r1 = (n-0.5)(lambda)
lambda=v/f
v=343m/s

The Attempt at a Solution



r2 and r1 are the distances from the speaker
so r2 is .517/2 + 1.96 = 2.2185
and r1 is .517/2 + 2.2185 = 2.477

i know i have to solve for frequency so i plugged (343m/s)/f into the equation

but then i got stuck. what do i plug in for n and how i change n for the lowest frequency and the next lowest?
 
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  • #2
nevermind, figured it out

DISREGARD THE QUESTION!
 
  • #3
Can you please tell me how to do this one? I've tried by using the equations but still can not figure it out.
Thanks!
 

1. What is the concept of "lowest frequency that produces an interference maximum"?

The lowest frequency that produces an interference maximum refers to the lowest frequency of a wave that can produce a constructive interference pattern when combined with another wave. This is a phenomenon that occurs when two waves with similar frequencies meet in phase, resulting in a higher amplitude.

2. How is the lowest frequency that produces an interference maximum calculated?

The calculation of the lowest frequency that produces an interference maximum involves determining the wavelength of the two waves and finding the point where they are in phase. This can be done using the equation λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency of the wave. The lowest frequency that produces an interference maximum will be the one that results in the two waves being in phase at the same point.

3. What is the significance of the lowest frequency that produces an interference maximum?

The lowest frequency that produces an interference maximum is significant because it represents the threshold at which constructive interference can occur. This means that any frequency lower than this value will result in destructive interference, where the two waves cancel each other out. It also helps scientists understand the behavior of waves and how they interact with each other.

4. Can the lowest frequency that produces an interference maximum vary?

Yes, the lowest frequency that produces an interference maximum can vary depending on the situation. It is determined by the wavelengths and phases of the two waves involved, which can be affected by factors such as the medium through which the waves are traveling. However, the speed of light is constant, so the frequency will always be inversely proportional to the wavelength.

5. How is the lowest frequency that produces an interference maximum used in practical applications?

The concept of the lowest frequency that produces an interference maximum is used in various practical applications, such as in the field of optics and telecommunications. It helps in the design and development of devices that utilize the principles of interference to produce certain effects or enhance signal transmission. It is also important in understanding the behavior of electromagnetic waves and their interactions with matter.

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