Question

Two sources of sound, Sį and S2, emit sound waves in phase at a frequency of 1000 Hz. They are separated by a distance d 2.0 m. If you were to move a detector along the x-axis starting at S1, how far would it have to be moved before it detects no sound at all? Take the speed of sound to be 343 m/s.

Answer 1

If we were to move a detector along the x-axis starting at S1, it would have to be moved 11.6m far before it detects no sound at all.

A sound wave is what?

A sound wave is a pressure wave, which may be conceptualized as variations in pressure over time. Transverse waves include sound waves. The tines of a tuning fork must transfer air from the fork to one's ear in order for one to hear the sound of the fork. The majority of sound waves, although not all of them, are produced by some sort of vibrating object.

What two forms of sound waves are there?

The characteristics of sound waves should be the starting point for studying sound. Transverse and longitudinal waves are the two fundamental forms of waves, and they are distinguished by how they move through space.

Given,

The two sources, $S_{1}$ and $S_{2}$ separated by a distance is d = 2.0m

$S_{2}P = \sqrt{x^{2} +2.0^{2} }$

       = $\sqrt{x^{2} +4}$

For destructive interference

$S_{2}P - S_{1}P$ = λ/2                                                    

 λ=ν/f

Given:

frequency  f = 1000hz

speed of sound ν = 343m/s

   =$\frac{343}{1000} = 0.343m$

$\sqrt{x^{2} +4} -x$ = $\frac{0.343}{2}$ = 0.1715

⇒ $\sqrt{x^{2} +4}$ = 0.1715 + x

⇒ $x^{2}$+4 = $(0.1715+x)^{2}$

           =      $(0.1715)^{2} + x^{2} + 2(0.1715)(x)$

⇒ 4 = $(0.1715)^{2}$+ 0.343 $x$

⇒ $x = \frac{4-0.1715^{2} }{0.343}$

       = 11.6m

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