Two small loudspeakers are placed about two meters apart in a large gymnasiumn a

Question

Two small loudspeakers are placed about two meters apart in a large gymnasiumn and are both driven by a source oscillating at a frequency of 343 Hz. One of the following statements is incorrect. Select it. The sound level refers to the sound level at the location indicated.

1.) Starting at a point closer to one loudspeaker and farther from the other and moving to a nearby point which is farther from both loudspeakers, the sound level could decrease or increase.

2.) The wavelength of the sound wave emitted by each loudspeaker is about 1 m.     

3.) Starting at a point closer to one loudspeaker and farther from the other and then moving to a nearby point which is closer to both loudspeakers, the sound level could decrease.

4.) At 10 m from one loudspeaker and 11 m from the other, the sound level is about the same as at a point 10.5 m from each loudspeaker.

5.) Starting at a point 14 m from each loudspeaker and then moving to a point 13 m from one loudspeaker and 13.5 meters from the other loudspeaker, the sound level increases.

Explanation / Answer

for the given problem

given, f = 343 Hz

a. Starting at a point closer to one loudspeaker and farther from the other and moving to a nearby point which is farther from both loudspeakers, the sound level could decrease or increase. This loudness would completely depend on the path difference and hence this statement is true

b. The wavelength of the sound wave emitted by each loudspeaker is about 1 m.

lambda*f = c

lambda = 343/343 = 1 m ( approximately)

so this statement is true

c. 3.) Starting at a point closer to one loudspeaker and farther from the other and then moving to a nearby point which is closer to both loudspeakers, the sound level could decrease. Again depending on relative distances form the both speakers this sound level could decrease as well as increase . hence this statement is true

d. At 10 m from one loudspeaker and 11 m from the other, the sound level is about the same as at a point 10.5 m from each loudspeaker.

as the wavelength of the sound wave is abotu 1 m, at 10 m and 11m, there is constructive interference and so is the case at 10.5 m from both of the loud speakers. But, at 10 m and 11 m there is a minima in constructive interference as well but 10.5 m does not have amonima, so thes eintensities will not be the same

hence this statement is false

e. Starting at a point 14 m from each loudspeaker and then moving to a point 13 m from one loudspeaker and 13.5 meters from the other loudspeaker, the sound level increases.

at 14 m from each speaker, there is 0 intensity from both speakeras because of the wavelength of the wave being 1 m. at 13.5 m there is destriuctive interference causing 0 amplitude . hence the sound level remains the same hence this statement is false

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