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Consider two sources of waves, as shown as Si and S2. These are placed on the y axXIS at +a/2 and -a/2 respectively. To find the wave amplitude at a point with polar coordinates (r,0)-which is the sum of the two waves arriving there, one from each source-you have to add the amplitudes. Let r, and r2 be the distances from the source points to the point p in question. (All students) If the two sources generate waves that are in phase, then from your reading, what has to be true about r, and r2 in order for the two waves to add up constructively at p? In other words, how must these two distances be related? (b) (Phys 212 and 252) The vector displacement S2 from the origin to source S, is j. The vector displacement from the origin to p with coordinates (x, y) is of course = xi + yj. Let be the vector displacement from S1 %3D to p. What is the relationship (a vector equation) between i and i ? (Phys 212 and 252) Use the result of the previous part to express the distance r, (not a vector) from S1 to p as a square root involving the polar coordinate angle 0 for point p. Write also a similar expression for r2 which is the distance from S2 to p. (Phys 212 and 252) Find the angles at which the two wave contributions add up constructively, i.e. at which they reinforce one another. (You should find two angles on each side of the straight ahead direction.)

Consider two sources of waves, as shown as Si and S2. These are placed on the y axXIS at +a/2 and -a/2 respectively. To find the wave amplitude at a point with polar coordinates (r,0)-which is the sum of the two waves arriving there, one from each source-you have to add the amplitudes. Let r, and r2 be the distances from the source points to the point p in question. (All students) If the two sources generate waves that are in phase, then from your reading, what has to be true about r, and r2 in order for the two waves to add up constructively at p? In other words, how must these two distances be related? (b) (Phys 212 and 252) The vector displacement S2 from the origin to source S, is j. The vector displacement from the origin to p with coordinates (x, y) is of course = xi + yj. Let be the vector displacement from S1 %3D to p. What is the relationship (a vector equation) between i and i ? (Phys 212 and 252) Use the result of the previous part to express the distance r, (not a vector) from S1 to p as a square root involving the polar coordinate angle 0 for point p. Write also a similar expression for r2 which is the distance from S2 to p. (Phys 212 and 252) Find the angles at which the two wave contributions add up constructively, i.e. at which they reinforce one another. (You should find two angles on each side of the straight ahead direction.)

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2. Consider two sources of waves, as shown as St and S2. These are placed on the y axis at +a/2 and -a/2 respectively. To find the wave amplitude at a point with polar coordinates (r,0)-which is the sum of the two waves arriving there, one from each source-you have to add the amplitudes. Let r, and r2 be the distances from the source points to the point p in question. (a) (All students) If the two sources generate waves that are in phase, then from your reading, what has to be true about r, and r2 in order for the two waves to add up constructively at p? In other words, how must these two distances be related? S1 (b) (Phys 212 and 252) The vector displacement S2 a from the origin to source Si is The vector displacement from the origin to p with coordinates (x, y) is of course 7 = xi +yj. Let be the vector displacement from S1 %3D to p. What is the relationship (a vector equation) between i and i ? (c) (Phys 212 and 252) Use the result of the previous part to express the distance r, (not a vector) from S, to p as a square root involving the polar coordinate angle 0 for point p. Write also a similar expression for r2 which is the distance from S2 to p. (d) (Phys 212 and 252) Find the angles at which the two wave contributions add up constructively, i.e. at which they reinforce one another. (You should find two angles on each side of the straight ahead direction.)
Transcribed Image Text:2. Consider two sources of waves, as shown as St and S2. These are placed on the y axis at +a/2 and -a/2 respectively. To find the wave amplitude at a point with polar coordinates (r,0)-which is the sum of the two waves arriving there, one from each source-you have to add the amplitudes. Let r, and r2 be the distances from the source points to the point p in question. (a) (All students) If the two sources generate waves that are in phase, then from your reading, what has to be true about r, and r2 in order for the two waves to add up constructively at p? In other words, how must these two distances be related? S1 (b) (Phys 212 and 252) The vector displacement S2 a from the origin to source Si is The vector displacement from the origin to p with coordinates (x, y) is of course 7 = xi +yj. Let be the vector displacement from S1 %3D to p. What is the relationship (a vector equation) between i and i ? (c) (Phys 212 and 252) Use the result of the previous part to express the distance r, (not a vector) from S, to p as a square root involving the polar coordinate angle 0 for point p. Write also a similar expression for r2 which is the distance from S2 to p. (d) (Phys 212 and 252) Find the angles at which the two wave contributions add up constructively, i.e. at which they reinforce one another. (You should find two angles on each side of the straight ahead direction.)
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