Phy 232
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Problem Number 5
Two sources separated by 6 meters emit waves with wavelength .66 meters emit waves in phase. The waves travel at identical velocities to a distant observer. At any point along the perpendicular bisector of the line segment connecting the two points, the two waves will arrive in phase an hence reinforce. What are the first three nonzero angles with the perpendicular bisector at which the first interference minimum will be observed?
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I am not sure what you mean when you ask for the first three nonzero angles. Are you asking for the location on the perpindicular bisector where maximum constructive interference occurs?
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This question is asking for the location relative to (not on) the perpendicular bisector where maximum constructive interference occurs.
Let me know if that doesn't clarify it.
Phy 232
Your 'question form' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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Problem Number 3
A string is under a tension of 11 Newtons and lies along the x axis. Beads with mass 7.1 grams are located at a spacing of 20 cm along a light but strong string. At a certain instant a certain bead is at y position .0026 meters, while the bead to its right is at y position .0019 meters and the bead to its left at y position .003 meters. At this instant the bead is moving in the y direction at .2633 m/s. Find the acceleration of the given bead and approximate its velocity .029 seconds later and the distance it will move in this time.
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We assumed that the strings weight is so light that it can be considered negligible, so each bead has a mass 7.1 g and is 20 cm apart so the mass density is 0.0355 kg/m.
Using the tension we found the velocity of the wave as 17.6028 m/s. We attempted to set up the wave equation placing our middle bead at x = 0 and that t = 0. By using the equation that we set up, we tried to solve for A and w using the position along the x-axis and the y-axis of our other two beads. This created two equations and two unknowns.
When we solved for our angular frequency we got several possible solutions and the one we used was 138.23 rad/s. We then tried to calculate A and got a negative number.
We aren't sure what we are doing wrong in this setup. Are we going in the right direction? Thanks.
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You don't describe your equation, so it's difficult to tell whether it's correct (or whether you are actually using the wave equation or some other equation you've identified as a wave equation--big difference). However your conception is good.
This question can be answered based on just the statics of the string. The string on each side of the bead exerts a force of 11 N, along the direction of the string. The angle of each string relative to horizontal is small, so the sine of the angle has a magnitude very close to the slope (this is because the hypotenuse and adjacent sides are practically the same length, so slope = rise / run = opposite side / adjacent side is practially the same as opposite side / hypotenuse). A carefully drawn and labeled picture which includes the bead and the two sections of string attached to it should make it easy to find the net force. (A quick mental estimate tells me that the force is around .0026 N, so acceleration would be a bit less than 4 m/s^2; if you get this chances are you're right (since we wouldn't be likely to agree if we weren't both right), but if you don't it doesn't mean you're wrong (it could easily be me)).
Let me know what you get, or if you have additional questions.