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Suppose that the separation between two speakers A and B is 4.80 m and the speakers are vibrating in-phase. They are playing identical 134-Hz tones and the speed of sound is 343 m/s. An observer is seated at a position directly facing speaker B in such a way that his line of sight extending to B is perpendicular to the imaginary line between A and B. What is the largest possible distance between speaker B and the observer, such that he observes destructive interference

Respuesta :

okpalawalter8

Answer:

[tex]X=8.44m[/tex]

Explanation:

From the question we are told that

Distance b/w A&B [tex]x=4.80m[/tex]

Frequency [tex]f=134Hz[/tex]

Sound speed [tex]v=343m/s[/tex]

Generally the equation for wavelength is mathematically given as

[tex]\lambda=v/f[/tex]

[tex]\lambda/2=1/2*v/f[/tex]

[tex]\lambda/2=1/2*\frac{343}{135}[/tex]

[tex]\lambda/2=1.27037037[/tex]

Generally the destructive interference X is mathematically given by

[tex]\sqrt{4.8^2 +X^2} -X=1.27037037\\[/tex]

[tex]23.04+BC^2=X^2+1.613+2.54*X[/tex]

Therefore the destructive interference is

[tex]X=8.44m[/tex]