Are you supposed to count nodes at the endpoints? The question as you've posted it does not even limit it to the space between the sources, so you could argue there's an infinity of each.superconduct said:Homework Statement
For two coherent sources vibrating in phase separated by 4.5(lambda), what are the numbers of antinodal and nodal lines?
Homework Equations
No. of nodal lines equals twice the floor function of separation over wavelength.
The Attempt at a Solution
No. of antinodal lines= 2(4)+1=9
No. of nodal lines= 2(4)=8
Is this correct?
What does it mean by endpoints here? How are there an infinity of nodal and antinodal lines? Under what conditions will the number be limited?haruspex said:Are you supposed to count nodes at the endpoints? The question as you've posted it does not even limit it to the space between the sources, so you could argue there's an infinity of each.
No, sorry, forget the bit about infinity.superconduct said:What does it mean by endpoints here? How are there an infinity of nodal and antinodal lines? Under what conditions will the number be limited?
Do you mean the two lines on the plane joining the sources and with a path difference of 4.5 lambda ?haruspex said:No, sorry, forget the bit about infinity.
But for the endpoints, I mean nodal lines straight out to the side from the two sources. In this set-up, if you move from one source directly away from the other source, they will cancel all the way along that line, no? Same for the other source. Are these two lines counted? The formula you quote implies not.
yessuperconduct said:Do you mean the two lines on the plane joining the sources and with a path difference of 4.5 lambda ?
If the separation becomes 4.4999999lamba instead of 4.5, then is my answer above correct?haruspex said:yes
Yes I think so, it's just the special case of n+1/2 I was asking about. It seems to me the formula you quote doesn't quite work there.superconduct said:If the separation becomes 4.4999999lamba instead of 4.5, then is my answer above correct?
The number of antinodal and nodal lines in a wave can be determined by analyzing the wavelength and frequency of the wave. The number of antinodal lines is equal to the number of half-wavelengths in the wave, while the number of nodal lines is equal to the number of whole wavelengths in the wave.
Antinodal and nodal lines represent areas of maximum and minimum amplitude, respectively, in a wave. They help to visualize the standing wave pattern and determine the energy distribution of the wave.
No, the number of antinodal and nodal lines can vary depending on the type of wave. For example, transverse waves have a different number of antinodal and nodal lines compared to longitudinal waves.
Antinodal lines are typically identified as points of maximum amplitude in a wave, while nodal lines are identified as points of minimum amplitude. They can be seen as alternating peaks and troughs in the wave pattern.
Yes, the number of antinodal and nodal lines can change as the wave propagates and interacts with its surroundings. For example, when a wave reflects off of a boundary, the number of antinodal and nodal lines may change due to interference effects.