Wave Amplitude from Line Source: Finding Amplitude at Distance '4r

In summary, the amplitude of a wave from a line source at a distance of '4r' will be 'a/2'. The wave-fronts spread out cylindrically and the field lines are radially outward. The loss in strength is inversely proportional to 'r'. The intensity is proportional to 1/r and the amplitude is proportional to the square-root of the intensity.
  • #1
altamashghazi
43
0

Homework Statement


from a line source, if amplitude of a wave at a distance 'r' is'a'.then the amplitude at a distance '4r' will be what?







The Attempt at a Solution


i could not understand the pattern of the spreading of the wave from the line source.
 
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  • #2
hi altamashghazi! :smile:
altamashghazi said:
i could not understand the pattern of the spreading of the wave from the line source.

the line is a cylinder

the wave-fronts spread out cylindrically :wink:
 
  • #3
what would be change in amplitude with distance. will it obey inverse square law?
 
  • #4
draw it! (from above) :rolleyes:

what happens to the field lines? :wink:
 
  • #5
i think they obey this law. am i right?
 
  • #6
altamashghazi said:
what would be change in amplitude with distance. will it obey inverse square law?

no!

the line is a cylinder

the wave-fronts spread out cylindrically​

draw it! (from above) …

what happens to the field lines?​
 
  • #7
wave fronts will be elliptical. then also it will follow inverse square law. bcoz area of ellipse is
π*a*b
 
  • #8
altamashghazi said:
wave fronts will be elliptical

why?? :confused:
 
  • #9
tiny-tim said:
why?? :confused:
sorry wavefronts will be cylinderical out wards but i couldn't guess the pattern of change in amplitude.
 
  • #10
altamashghazi said:
sorry wavefronts will be cylinderical out wards

yes! :smile:

ok, then how is the surface area of a cylinder related to radius? :wink:
 
  • #11
tiny-tim said:
yes! :smile:

ok, then how is the surface area of a cylinder related to radius? :wink:

it is directly proportional to r.
A=2πr(h+r)
 
  • #12
ok :smile:, so if you draw the field lines, they'll all be radially outward,

and the number going through any wavefront will be proportional to r …

so what is the loss in strength?​
 
  • #13
tiny-tim said:
ok :smile:, so if you draw the field lines, they'll all be radially outward,

and the number going through any wavefront will be proportional to r …

so what is the loss in strength?​

it will be inversely proportional to r.
i mean answer should be a/4
 
  • #14
yup! :smile:
 
  • #15
tiny-tim said:
yup! :smile:
but its wrong the answer is a/2. therefore i m confused. pls help.
 
  • #16
oh, I'm sorry, i thought a was the intensity :redface:

the intensity (as shown by field lines) is proportional to 1/r,

and the amplitude is proportional to the square-root of the intensity :smile:
 
  • #17
tiny-tim said:
oh, I'm sorry, i thought a was the intensity :redface:

the intensity (as shown by field lines) is proportional to 1/r,

and the amplitude is proportional to the square-root of the intensity :smile:
thank u very mucch
 
  • #18
tiny-tim said:
oh, I'm sorry, i thought a was the intensity :redface:

the intensity (as shown by field lines) is proportional to 1/r,

and the amplitude is proportional to the square-root of the intensity :smile:

thank u very much
 

Related to Wave Amplitude from Line Source: Finding Amplitude at Distance '4r

1. What is a line source?

A line source is a hypothetical source of waves that extends infinitely in one dimension. It is often used in physics to simplify the analysis of wave behavior.

2. How is amplitude calculated for a wave from a line source?

The amplitude of a wave from a line source is calculated using the formula A = Ar/4r, where A is the amplitude at distance r, Ar is the amplitude at the source, and r is the distance from the source.

3. Why is the amplitude at distance 4r significant?

The amplitude at distance 4r is significant because it represents the point where the wave has traveled four times the distance from the source and has spread out to form a quarter-circle. This distance is often used in calculations for wave behavior.

4. Can the amplitude at distance 4r be negative?

Yes, the amplitude at distance 4r can be negative. This means that the wave has undergone a phase shift of 180 degrees and the displacement of the wave is in the opposite direction from the source.

5. How does the amplitude change as distance from the line source increases?

The amplitude decreases as the distance from the line source increases. This is due to the spreading out of the wave over a larger area as it travels further from the source.

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