Two identical loudspeakers that are 5.00 m apart and face toward each other are driven in phase by the same oscillator at a frequency of 875 Hz. The speed of sound in the room is 344 m/s. If you start out standing midway between the speakers, find the shortest distance you can walk toward either speaker in order to hear a minimum of sound.

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nuuk nuuk · Answer 1 · 2019-10-15T06:40:49+02:00

Answer:0.0982 m

Explanation:

Given

distance between two loudspeaker is 5 m

frequency (f )=875 Hz

speed of sound (v)=344 m/s

Let [tex]x_0[/tex] be the smallest distance moved by observer then

Position of observer w.r.t to first speaker is

[tex]x_1=\frac{L}{2}-x_0[/tex]

Position of observer w.r.t to second speaker is

[tex]x_2=\frac{L}{2}+x_0[/tex]

[tex]\Delta x=2x_0[/tex]

For Destructive interference

[tex]\Delta x=\left ( m+\frac{1}{2}\right )\cdot lambda[/tex]

For minimum m=0

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

[tex]2x_0=\frac{v}{2f}[/tex]

[tex]x_0=\frac{v}{4f}=\frac{344}{4\times 875}=0.0983 m[/tex]