A manufacturing firm has hired your company, Acoustical Consulting, to help with a problem. Their employees are complaining about the annoying hum from a piece of machinery. Using a frequency meter, you quickly determine that the machine emits a rather loud sound at 1200 Hz. After investigating, you tell the owner that you cannot solve the problem entirely, but you can at least improve the situation by eliminating reflections of this sound from the walls. You propose to do this by installing mesh screens in front of the walls. A portion of the sound will reflect from the mesh; the rest will pass through the mesh and reflect from the wall. How far should the mesh be placed in front of the wall for this scheme to work?

Step by step solution

01

The concept of the reflection of the sound 

The reflective sound is mainly known as an echo in which the voice gets comes back from the other end by the reflection.

02

Understanding the scheme 

Based on the destructive wavefront interference the phase difference is $∆\varnothing =2\mathrm{\pi }\frac{∆\mathrm{\pi }}{\mathrm{\lambda }}=(2\mathrm{n}+1)\mathrm{\pi }$

The distance that will work is $∆x=\frac{(2\mathrm{n}+1)\lambda }{2}$thus the smallest distance will be $\lambda /4$and to find $\lambda$the equation will be $\lambda =\frac{v}{f}=\frac{340}{1200}=28.3cm$

Thus, the mesh spread will be$\boxed{d=7.08cm}$

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