Understanding Waves: Questions on Phase Differences and Interference Patterns

[WesleyHuang]

1.
Sources A and B emit long-range radio waves of wavelength 320 m, with the phase of the emission from A ahead of that from source B by 90°. The distance r_A from A to a detector is greater than the corresponding distance r_B from B by 82 m. What is the magnitude of the phase difference at the detector?


2.
In a double-slit experiment the distance between slits is 5.2 mm and the slits are 0.82 m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 450 nm, and the other due to light of wavelength 580 nm. What is the separation in meters on the screen between the m = 4 bright fringes of the two interference patterns?



The first one is actually an online-test question. I have tried 3 times using the method from the textbook, but i still haven't got the right answer. Can anyone help me? THANKS!

 

[HallsofIvy]

You understand, don't you, that you have to show what you have done yourself?

 

[WesleyHuang]

You understand, don't you, that you have to show what you have done yourself?

Hello! What i have done for the first question is:
devide the wave length 320m by 4, since A is 90° ahead (a quarter of a cycle)
then I take 82m away from it, since the wave from source A goes 82m further
finally i just take the ratio of the phase difference with the wavelength and multiply the result by 2π in order to convert the unit to radian.

is it correct?

 

[WesleyHuang]

i can't do the second one. i thought the 2 lights will not have any bright fringes, because the wavelengths are different, double-slit interference will not occur...
do you think so?

 

[Asteroid1]

Tips:
1. How much is A in front of B? (90 deg)
How big is the phase difference between A and B just because wave A has to travel longer?

2. For both 450 nm and 580 nm a double-slit interference will occur. What distance for m=4 at 450 nm and what distance for the 580 nm wave?

 

[WesleyHuang]

I've got the answers now! thanks!