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question 1) Two identical loudspeakers, A and B, are 3.00-m apart. The loudspeakers are driven by...

question 1)

Two identical loudspeakers, A and B, are 3.00-m apart. The loudspeakers are driven by the same amplifier and emit 900-Hz sound waves in all directions. Take the speed of sound in air to be 344 m/s. A small microphone is moved out from point B along a line perpendicular to the line connecting A and B.

a) At what distances from B will there be destructive interference?

b) At what non-infinite distances from B will there be constructive interference?

question 2)

An electromagnetic wave with frequency 120 Hz travels in an insulating magnetic material that has dielectric constant 3.00 and relative permeability 5.00 at this frequency. The electric field has amplitude 7.5Ý10-2V/m.

a) What is the speed of propagation of the wave?

b) What is the wavelength of the wave?

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Answer #1

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Answer #2

1. Wavelength of the sound wave = v/ f = 344/900 = 0.38222 m
So, when the hypotenuse(distance of mic from A) = n*0.38222, constructive interference is there and destructive interference is there when it is (n+0.5)*0.38222
Now, 3/0.38222 = 7.85
So, atleast n = 8 for,  constructive interference, distance from B = ((8*0.38222)2 - 32)1/2 = 0.5916 m (b)
So, atleast n = 8.5 for destructive interference , distance from B = ((8.5*0.38222)2 - 32)1/2 = 1.247 m... (a)
2.
The velocity = c/(3*5)1/2 = 77459666.92 m/s
So, wavelength = velocity / frequency = 77459666.92 / 120 = 645497.2244 m

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