Question

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

Answer 1

Answer:

$X=8.44m$

Explanation:

From the question we are told that

Distance b/w A&B $x=4.80m$

Frequency $f=134Hz$

Sound speed $v=343m/s$

Generally the equation for wavelength is mathematically given as

$\lambda=v/f$

$\lambda/2=1/2*v/f$

$\lambda/2=1/2*\frac{343}{135}$

$\lambda/2=1.27037037$

Generally the destructive interference X is mathematically given by

$\sqrt{4.8^2 +X^2} -X=1.27037037$

$23.04+BC^2=X^2+1.613+2.54*X$

Therefore the destructive interference is

$X=8.44m$