Homework Help: Wave amplitude

1. Mar 5, 2012

altamashghazi

1. The problem statement, all variables and given/known data
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?

3. The attempt at a solution
i could not understand the pattern of the spreading of the wave from the line source.

2. Mar 5, 2012

tiny-tim

hi altamashghazi!
the line is a cylinder

3. Mar 5, 2012

altamashghazi

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

4. Mar 5, 2012

tiny-tim

draw it!! (from above)

what happens to the field lines?

5. Mar 12, 2012

altamashghazi

i think they obey this law. am i right?

6. Mar 12, 2012

tiny-tim

no!

the line is a cylinder

the wave-fronts spread out cylindrically ​

draw it!! (from above) …

what happens to the field lines?​

7. Mar 12, 2012

altamashghazi

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

8. Mar 12, 2012

tiny-tim

why??

9. Mar 12, 2012

altamashghazi

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

10. Mar 12, 2012

tiny-tim

yes!

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

11. Mar 12, 2012

altamashghazi

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

12. Mar 12, 2012

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?​

13. Mar 12, 2012

altamashghazi

it will be inversely proportional to r.
i mean answer should be a/4

14. Mar 12, 2012

tiny-tim

yup!

15. Mar 12, 2012

altamashghazi

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

16. Mar 12, 2012

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

17. Mar 12, 2012

altamashghazi

thank u very mucch

18. Mar 12, 2012

altamashghazi

thank u very much