Question

There are two speakers at the front of the room. Each is outputting a 250Hz pure tone. For each of the following situations, will you hear constructive interference (a loud noise) or destructive interference (soft or no noise). ? represents the wavelength of the 250Hz tone.
Constructive Destructive  You are 2.5? away from speaker A; 3? away from speaker B and at the speakers the waves are exactly in phase.
Constructive Destructive  You are 3? away from speaker A; 2? away from speaker B and at the speakers the waves are exactly out of phase.
Constructive Destructive  You are 3? away from speaker A; 2.5? away from speaker B and at the speakers the waves are exactly out of phase.
Constructive Destructive  You are 2? away from speaker A; 3? away from speaker B and at the speakers the waves are exactly in phase.

There are two speakers at the front of the room. Each is outputting a 250Hz pure tone. For each of the following situations, will you hear constructive interference (a loud noise) or destructive interference (soft or no noise). ? represents the wavelength of the 250Hz tone.
Constructive Destructive  You are 3.5? away from speaker A; 3? away from speaker B and at the speakers the waves are exactly in phase.
Constructive Destructive  You are 2.5? away from speaker A; 3? away from speaker B and at the speakers the waves are exactly out of phase.
Constructive Destructive  You are 2? away from speaker A; 3? away from speaker B and at the speakers the waves are exactly in phase.
Constructive Destructive  You are 6? away from speaker A; 5? away from speaker B and at the speakers the waves are exactly out of phase.

Answer 1

the condition for constructive interference,

path difference=n*lambda (where, n=0, 1, 2, 3 ...)

the conditon for destructive interference,

path difference=(2n-1)*lambda/2 (where, n=1, 2, 3 ...)

part (A)

a)

path difference=3*lambda-2.5*lambda

=1/2*lambda

answer is: destructive

b)

path difference=3*lambda-2*lambda

=1*lambda

here,

waves are in out of phase

path difference=lambda+lambda/2

=3/2*lambda

answer is: destructive

c)

path difference=3*lambda-2.5*lambda

=1/2*lambda

here,

waves are in out of phase

path difference=lambda/2+lambda/2

=1*lambda

answer is: constructive

d)

path difference=3*lambda-2*lambda

=1*lambda

answer is: constructive

part (B)

a)

path difference=3.5*lambda-3*lambda

=1/2*lambda

answer is: destructive

b)

path difference=3*lambda-2.5*lambda

=1/2*lambda

here,

waves are in out of phase

path difference=lambda/2+lambda/2

=1*lambda

answer is: constructive

c)

path difference=3*lambda-2*lambda

=2*lambda

answer is: constructive

d)

path difference=6*lambda-5*lambda

=1*lambda

here,

waves are in out of phase

path difference=lambda+lambda/2

=3/2*lambda

answer is: desstructive