Imagine you are in an open field where two loudspeakers are set up and connected

Question

Imagine you are in an open field where two loudspeakers are set up and connected to the same amplifier so that they emit sound waves in phase at 688 Hz. Take the speed of sound in air to be 344 m/s.

Part A

If you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left, will the sound that you hear be louder than the sound you would hear if only one speaker were in use?

Imagine you are in an open field where two loudspeakers are set up and connected to the same amplifier so that they emit sound waves in phase at 688 Hz. Take the speed of sound in air to be 344 m/s.

Part A

If you are 3.00 m from speaker A directly to your right and 3.50 m from speaker B directly to your left, will the sound that you hear be louder than the sound you would hear if only one speaker were in use?

Explanation / Answer

Part (A), correct oprion is : yes

beacause,

frequency, f=688 Hz

speed, v=344 m/sec

wavelength, lambda=v/f

lambda=344/688

lambda=0.5 m ---(1)

and

the distance between person and speaker A is r1=3m

the distance between person and speaker B is r2=3.5m

===>

path difference, d= r2-r1

=3.5-3

=0.5 m ----(2)

therefore,

from equation (1) and (2),

path difference is equal to lambda

hence, sound wave forms the constuctive interference

and the sound will be louder

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