Answer:
a. constructive interference takes place.
b. x = 0.34 m= 34 cm
c.. [tex]x=0.69m = 69cm[/tex]
Explanation:
Given
Distance between speakers = 12.0 m
frequency = 245 Hz,
speed of sound = 340 m/s,
a. For constructive interference we have
the path difference is [tex]= m\lambda[/tex]
where m = +/-1,+/-2,+/-3,..........
Wavelength of sound = [tex]=\frac{v}{f} =340/245=1.38 m[/tex]
As women is at center or middle point, therefore the path difference at that point must be zero
[tex]d_{2} -d_{1}=0[/tex]
Now the path difference [tex]d_{2} -d_{1}=0[/tex] is an integral multiple of the wavlenght therefore constructive interference takes place.
b.
for the sound to reach a minimum intensity
Now if she moves x distance from current point then
[tex]d_{2}^{'}-d_{1}^{'}=(d_{2} +x) - (d_{1} -x)[/tex]
[tex]d_{2}^{'}-d_{1}^{'} =2x[/tex]
for hearing minimum intensity the interference must be destructive therefore,
[tex]d_{2}^{'}-d_{1}^{'}= (m+\frac{1}{2})\lambda[/tex]
for m = 0
[tex]d_{2}^{'}-d_{1}^{'}= (0+\frac{1}{2})\lambda[/tex]
by putting the value of lamda = 1.38 and difference in distance as 2x
we get
x = 0.34 m= 34 cm
c.
for the sound to reach a maximum intensity
[tex]d_{2}^{'}-d_{1}^{'}= m\lambda[/tex]
for that m=1
[tex]d_{2}^{'}-d_{1}^{'}= 1\lambda[/tex]
[tex]2x= \lambda[/tex]
[tex]x=\frac{\lambda}{2}[/tex]
[tex]x=\frac{1.38}{2}[/tex]
[tex]x=0.69m = 69cm[/tex]
