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

[altamashghazi]

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.

 

[tiny-tim]

hi altamashghazi!

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 ​

 

[altamashghazi]

what would be change in amplitude with distance. will it obey inverse square law?

 

[tiny-tim]

draw it! (from above) …

what happens to the field lines? ​

 

[altamashghazi]

i think they obey this law. am i right?

 

[tiny-tim]

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?​

 

[altamashghazi]

wave fronts will be elliptical. then also it will follow inverse square law. bcoz area of ellipse is
π*a*b

 

[tiny-tim]

wave fronts will be elliptical

why??

 

[altamashghazi]

why??

sorry wavefronts will be cylinderical out wards but i couldn't guess the pattern of change in amplitude.

 

[tiny-tim]

sorry wavefronts will be cylinderical out wards

yes!

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

 

[altamashghazi]

yes!

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

it is directly proportional to r.
A=2πr(h+r)

 

[tiny-tim]

ok , 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?​

 

[altamashghazi]

ok , 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

 

[tiny-tim]

yup!

 

[altamashghazi]

yup!

but its wrong the answer is a/2. therefore i m confused. pls help.

 

[tiny-tim]

oh, I'm sorry, i thought a was the intensity

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

and the amplitude is proportional to the square-root of the intensity ​

 

[altamashghazi]

oh, I'm sorry, i thought a was the intensity

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

and the amplitude is proportional to the square-root of the intensity ​

thank u very mucch

 

[altamashghazi]

oh, I'm sorry, i thought a was the intensity

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

and the amplitude is proportional to the square-root of the intensity ​

thank u very much