"Point S1 and S2 are close sources of circular water waves each of wavelength 6.0cm. P is a point some distance away from the sources. Explain whether the following path differences (path difference = PS2 - PS1) result in nodes or anti-nodes.
a) 6.0cm
b) 9.0cm
c) 18cm
d) 21cm"
I am very confused. What am I supposed to do?
if the path length is a multiple of a wavelength, reinforcement (anti-node) occurs, if it is a odd number of half-wavelengths, it is destructive and a node results.
for instance d) Not a multiple of 6cm, but it is ...18+3 or 6*3+3 which means it is a halflength left over, destructive.
Ah! Thank you so much!
To determine whether the given path differences result in nodes or anti-nodes, you need to understand the concept of interference in wave physics.
When two waves meet, they interfere with each other either constructively (leading to the formation of an anti-node) or destructively (leading to the formation of a node). The interference pattern depends on the phase difference between the waves, which is determined by the path difference between the sources and the point of interest.
In this case, you have two close sources, S1 and S2, emitting circular water waves with a wavelength of 6.0 cm. Let's consider the path difference between the two sources.
a) Path difference = 6.0 cm:
If the path difference is equal to one wavelength (6.0 cm), the waves from both sources will reach the point P in-phase, resulting in constructive interference. This means that there will be an anti-node at point P.
b) Path difference = 9.0 cm:
If the path difference is one and a half wavelengths (9.0 cm), the waves from the two sources will reach point P with a phase difference of half a wavelength. This leads to destructive interference and the formation of a node.
c) Path difference = 18 cm:
If the path difference is equal to three wavelengths (18 cm), the waves from the sources will meet in-phase at point P, resulting in constructive interference and the formation of an anti-node.
d) Path difference = 21 cm:
If the path difference is equal to three and a half wavelengths (21 cm), the waves from the sources will meet with a phase difference of half a wavelength, leading to destructive interference and a node at point P.
In summary, a path difference equal to a whole number of wavelengths (0 cm, 6 cm, 12 cm, etc.) results in constructive interference and an anti-node. A path difference equal to a half wavelength (3 cm, 9 cm, 15 cm, etc.) leads to destructive interference and a node.