You are walking around a large open field. The only objects nearby are two ident

Question

You are walking around a large open field. The only objects nearby are two identical speakers set some distance apart, which are both producing sound, in unison, with a wavelength of 4 m. As you wander around the field, you notice that at certain locations, the sound you hear is surprisingly loud, while at others it seems unusually quiet. You conclude that you are observing the effects of interference between the two sources of sound waves. For each of the locations given below, indicate what sort of interference would occur at that point.

Constructive Interference, Destructive Interference, or In Between:

12m from one speaker and 14 from the other

21 from one speaker and 15 from the other

13 from one speaker and 18 from the other

16 from one speaker and 13 from the other

9 from one speaker and 13 from the other

8 from each speaker

16 from one speaker and 24 from the other

Explanation / Answer

We know that wehave a relation phase diffrence and path diffrence

DeltaQ =2pi/lamda(x1-x2)

We get constructive interfrence for the values fi =0,2pi,4pi,6pi....

and destructive interference for fi =pi,3pi,5pi,7pi and soo on

Given that lamda =4m

Now pahse diffrence is

12m from one speaker and 14 from the other then fi =2pi/4(14-12) =pi (desturctive)

21 from one speaker and 15 from the other then fi =2pi/4(21-15) =3pi (desturctive)

13 from one speaker and 18 from the other the fi =2pi/4(18-13) =2.5pi (in Between)

16 from one speaker and 13 from the other the fi =2pi/4(16-13) =1.5pi (in Between)

9 from one speaker and 13 from the other the fi =2pi/4(13-9) =2pi (constructive)

8 from each speaker fi =2pi/4(8-8) =0 (constructive)

16 from one speaker and 24 from the other then fi =2pi/4(24-16) =4pi (constructive)

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