A square is 7.2 m on a side, and point A is the midpoint of one of the sides. On

Question

A square is 7.2 m on a side, and point A is the midpoint of one of the sides. On the side opposite this spot, two in-phase loudspeakers are located at adjacent corners, as shown in the figure. Standing at point A, you hear a loud sound because constructive interference occurs between the identical sound waves coming from the speakers. As you walk along the side of the square toward either empty corner, the loudness diminishes gradually but does not entirely disappear until you reach either empty corner, where you hear no sound at all. Thus, at each empty corner destructive interference occurs.

Concepts:

(i) Why does constructive interference occur at point A?

The distances that the sound waves travel differ by zero wavelengths.

The distances that the sound waves travel differ by one half-wavelength.

The distances that the sound waves travel differ by one wavelength.

The distances that the sound waves travel differ by three half-wavelengths.

The distances that the sound waves travel differ by two wavelengths.

(ii) What is the general condition that leads to destructive interference?

The distances that the sound waves travel differ by an integer number of half-wavelengths.

The distances that the sound waves travel differ by an odd integer number of wavelengths.

The distances that the sound waves travel differ by an odd integer number of half-wavelengths.

The distances that the sound waves travel differ by an integer number of wavelengths.

(iii) The condition that leads to destructive interference entails a number of possibilities. Which of them applies at either empty corner of the square?

The distances that the sound waves travel differ by zero wavelengths.

The distances that the sound waves travel differ by one half-wavelength.

The distances that the sound waves travel differ by one wavelength.

The distances that the sound waves travel differ by three half-wavelengths.

The distances that the sound waves travel differ by two wavelengths.

Calculation: Find the wavelength of the sound waves. (m)

Explanation / Answer

i) The constructive interference occur at point A as the distances that the sound waves travel differ by zero wavelengths.

ii)  the general condition that leads to destructive interference is the distances that the sound waves travel differ by an odd integer number of half-wavelengths.

iii) The condition that leads to destructive interference is The distances that the sound waves travel differ by one half-wavelength

Calculation:

At any corner, L1=7.2m, L2=7.2*1.414=10.18 m

So at any empty corner for destructive interference,

L2-L1=Wavelength/2=2.98

Wavelength=5.96 m

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