Destructive interference of sound

In summary, in a room with dimensions of 3.5 m by 7.0 m and a temperature of 22°C, two loudspeakers separated by 0.50 m on one wall emit a constant amplitude sound of frequency 690 Hz, in phase with each other and radiating equally in all directions. The shortest distance x along the adjacent wall where an observer will hear no sound can be found by using constructive interference, where the lengths differ by an odd multiple of half the wavelength (0.249 m). By replacing x^2 + 9 with the new variable y, solving for √y and finding the k that gives the smallest possible value, the computed value for x is nonreal, with the
  • #1
sparkle123
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0
Two loudspeakers are separated by 0.50 m on one wall of a room measuring 3.5 m by 7.0 m at a temperature of 22°C. Both speakers generate a constant amplitude sound of frequency 690 Hz, in phase with each other, radiating equally in all directions. What is the shortest distance x along the adjacent wall where an observer will hear no sound? Ignore any reflections from the walls.

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I think that constructive interference means the lengths differ by an odd multiple of half the wavelength (0.249 m).
so sqrt(x^2 + 3.5^2) - sqrt(x^2 + 3^2) = 0.249 (2k + 1)

But this is really complicated...Please give me a hint on how to start?
 
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  • #2
Life is easier if you replace x2+9 by a new variable, say y. Move √y to the right-hand side and square the equation, y will cancel. Solve for √y. Decide what k gives the smallest possible value for it, then compute x.

ehild
 
  • #3
Thanks, but I get a nonreal answer for x. the min of y is 1.064E-12
 

FAQ: Destructive interference of sound

1. What is destructive interference of sound?

Destructive interference of sound is when two or more sound waves of similar frequencies come together and cancel each other out, resulting in a decrease in the overall sound level. This occurs when the peaks of one wave align with the troughs of another wave, causing them to cancel out.

2. How does destructive interference affect sound?

Destructive interference can significantly reduce the amplitude, or loudness, of a sound. This can result in a quieter or distorted sound, depending on the severity of the interference. It can also affect the overall quality of the sound by causing phase shifts and changes in frequency.

3. What causes destructive interference of sound?

Destructive interference of sound can be caused by a variety of factors, including the distance between sound sources, the direction and angle of the sound waves, and the properties of the medium through which the sound travels. It can also occur when sound waves bounce off of surfaces and interfere with each other.

4. Can destructive interference be beneficial?

While it is often seen as a negative phenomenon, destructive interference can actually be beneficial in some cases. In noise-canceling technology, for example, destructive interference is intentionally used to cancel out unwanted background noise and improve the overall sound quality.

5. How can destructive interference of sound be prevented?

There are a few ways to prevent destructive interference of sound. One method is to carefully position sound sources and speakers to avoid overlapping and canceling each other out. Another approach is to use sound-absorbing materials to reduce the reflection of sound waves. Additionally, adjusting the frequency or phase of sound waves can also help prevent destructive interference.

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