All objects are on the x-axis. A speaker is at a location of -2.0 meters. An obs
ID: 1549050 • Letter: A
Question
All objects are on the x-axis. A speaker is at a location of -2.0 meters. An observer is at 5.0 meters. A second speaker is to the right of the observer, but can be moved. Both speakers emit sound with a wavelength of 2.5 meters.
a) Determine the path difference in terms of the location of the second speaker.
b) Specify two locations for the second speaker which create constructive interference for the observer (or state that two such locations do not exist). Show your work or you will not earn full credit even if your answer is correct..
c) Specify two locations for the second speaker which create destructive interference for the observer (or state that two such locations do not exist) . Show your work or you will not earn full credit even if your answer is correct..
d) Specify two locations for the second speaker which create neither constructive nor destructive interference for the observer (or state that two such locations do not exist) . Show your work or you will not earn full credit even if your answer is correct..
Explanation / Answer
From the given question,
(a)Let the second observer be x m from origin.
distance between first observer and speaker=7m
distance between second observer and speaker=(x-5)m
path difference= (x-5) -7=(x-12)m
(b)for constructive interference the path difference should be 0 or multiple of wavenength
so, second observer should be
x-12=0, or x=12m from origin towards right.
x-12=2.5, or x=14.5m from origin towards right.
(c)for destructive interference the path difference should be odd multiple of wavenength/2
so, second observer should be
x-12=(2.5/2), or x=13.25m from origin towards right.
x-12=3(2.5/2), or x=15.75m from origin towards right.
(d) for neither constructive nor destructive interference, the phase difference should be 120 degrees or path difference should be wavelength/3
x-12=(2.5/3), or x=12.83m from origin towards right.
x-12=4(2.5/3), or x=15.33m from origin towards right.