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.)

7. 8. 9. PQ represents the boundary between regions I and II, having different depths, in a ripple tank containing water. Wave fronts are shown crossing the boundary. (a) (b) (c) (d) (e) I NOTE: v represents wave velocity A represents wavelength f represents frequency T represents period II (a) (b) (c) (d) (e) Which of the following correctly describes the waves in region II as compared to those in region I? In region II, f is the same, v is less, and A is less than in region I. In region II, f is the same, v is greater, and A is greater than in region 1. In region II, f is the same, v is greater. and A is less than in region I. In region II, v is the same, T is less, and A is less than in region I. In region II, v is the same, T is greater, and A is less than in region I. When two point sources placed a fixed distance apart vibrate in phase, nodal lines are produced. Which one of the following statements concerning these lines is incorrect? Energy is transmitted away from the sources…

Show by direct substitution that the exponential Gaussian function defined by ?(x,t) = ae-(bx-ct)^2 satisfies the wave equation: (?2?(?,?))/(?x2) = (1/v2) * (?2?(x,t))/(?t2) if the wave is given by the v = (c/b) and a, b, and c are constants.

Two harmonic waves are given by: y1=Acos(kx−ωt) and y2=Asin(kx−wt+π/3) where k=5πm−1, ω=800πs−1 and A=4.0cm  sin(theta1) +/- sin(theta2) = 2sin( (theta1 +/- theta2) /2) cos( (theta1 -/+ theta2) /2) Using the provided identity, find the equation of the resultant wave and its amplitude.  Show all work.

A wave propagation is represented by y = 4 sin (20nt – x) where x is in cm and t is in s. Calculate the 4. (a) (b) (c) Wavelength Frequency Velocity [1 = 12 m; f = 10 Hz; v = 120 ms-1]

S A person stands 13.00 m from a speaker, and 8.00 m from an identical speaker. What is the wavelength of the first (n=1) interference maximum (constructive)? (Speed of sound = 343 m/s) (Unit = m) demy of Science. All Rights Reserved. =h H K hulu 20 Enter New ✔