Two Speakers - Sound Maximum and Sound Minimum Problem

In summary, the problem states that two loudspeakers 5.0 m apart are playing the same frequency, and when standing 13.0 m in front of them, centered between them, a sound of maximum intensity is heard. When walking parallel to the plane of the speakers, staying 13.0 m in front of them, a minimum of sound intensity is heard when directly in front of one of the speakers. Using the equations for sound maximum and minimum, the frequency of the sound is calculated to be 246.3104195 Hz.
  • #1
davichi
2
0
[Solved] Two Speakers - Sound Maximum and Sound Minimum Problem

Hi, I am having difficulty solving the following problem:

Homework Statement



Two loudspeakers 5.0 m apart are playing the same frequency. If you stand 13.0 m in front of the plane of the speakers, centered between them, you hear a sound of maximum intensity. As you walk parallel to the plane of the speakers, staying 13.0 m in front of them, you first hear a minimum of sound intensity when you are directly in front of one of the speakers.

What is the frequency of the sound? Assume a sound speed of 340 m/s.


Homework Equations



Sound Maximum:
L1 - L2 = n[tex]\lambda[/tex]

Sound Minimum:
L1' - L2 = (n+[tex]\frac{1}{2}[/tex])[tex]\lambda[/tex]

Frequency:
f = [tex]\frac{v}{\lambda}[/tex]

The Attempt at a Solution



diagram.jpg


Sound Maximum:
L1 - L2 = n[tex]\lambda[/tex]

L2 = 13.0 m
L1 = [tex]\sqrt{13.0^{2}+2.50^{2}}[/tex] = 13.23820229

L[tex]_{1}[/tex] - L[tex]_{2}[/tex] = n[tex]\lambda[/tex]
13.23820229 - 13 = n[tex]\lambda[/tex]
n[tex]\lambda[/tex] = 0.23820229

Sound Minimum
L1' - L2 =(n + [tex]\frac{1}{2}[/tex])[tex]\lambda[/tex]

L2 = 13.0 m
L1' = [tex]\sqrt{13.0^{2}+5.0^{2}}[/tex] = 13.92838828

Sub in n[tex]\lambda[/tex]= 0.23820229:

L1' - L2 = (n + [tex]\frac{1}{2}[/tex])[tex]\lambda[/tex]
13.92838828 - 13 = n[tex]\lambda[/tex] + [tex]\lambda[/tex]/2
[tex]\lambda[/tex]/2 = 0.92838828 - 0.23820229
[tex]\lambda[/tex] = 1.380371974

Sub in [tex]\lambda[/tex] = 1.380371974:
f = [tex]\frac{v}{\lambda}[/tex]
f = [tex]\frac{340}{1.380371974}[/tex]
f = 246.3104195 Hz

I'm not sure if my approach is wrong or if I'm interpreting the question incorrectly. Any help would be greatly appreciated!

Thanks.
 
Last edited:
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  • #2
In the central position the two speakers are at equal distance. So the path difference is zero. In between the first and the second position, there is neither a maximum nor a minimum. So at the second position ( l1' - l2) = λ/2.
 
  • #3
Ooh.. no wonder. Thank you very much!
 

1. What is the "Two Speakers - Sound Maximum and Sound Minimum Problem"?

The "Two Speakers - Sound Maximum and Sound Minimum Problem" is a common issue faced by audio engineers and sound system designers. It refers to the challenge of finding the optimal placement of two speakers in a room to achieve the maximum and minimum sound levels at specific locations.

2. Why is it important to solve this problem?

Solving the "Two Speakers - Sound Maximum and Sound Minimum Problem" is important because it ensures an even distribution of sound throughout a room, providing a better listening experience for the audience. It also helps prevent sound distortion and feedback, which can be detrimental to the quality of the sound.

3. What factors affect the sound levels in this problem?

There are several factors that can affect the sound levels in the "Two Speakers - Sound Maximum and Sound Minimum Problem," including the distance between the speakers, the distance from the speakers to the audience, the size and shape of the room, and the frequency response of the speakers.

4. How can this problem be solved?

There are several methods for solving the "Two Speakers - Sound Maximum and Sound Minimum Problem." One approach is to use mathematical equations and computer simulations to determine the optimal placement of the speakers. Another method is to use trial and error by physically moving the speakers and testing the sound levels at different locations in the room.

5. Are there any tools or software available to help solve this problem?

Yes, there are various tools and software available to help solve the "Two Speakers - Sound Maximum and Sound Minimum Problem." Some examples include acoustic modeling software, speaker placement calculators, and sound level meters. These tools can assist in determining the best placement of the speakers to achieve the desired sound levels in a room.

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