Two waves, yı = (2.9 mm) sin [(22.1 rad /m)x – (540 rad/s)t] and y2 = (1.3 mm) sin [(22.1 rad /m)x + (540 rad /s)] travel along a stretched string. (a) Find the resultant wave y = y1+ y2 as a function of t for x = 0 and 1/2 where is the wavelength. Omit units. (b) The resultant wave is the superposition of a standing wave and a traveling wave. In which direction does the traveling wave move?...
005 10.0 points Two harmonic waves are described by yı = A sin(kr + wt) y2 = A sin(kr-wt), where A=4 m, k = 2 m , and w=8s. What is the maximum amplitude of the resultant waves at the position of 2.9 m along the r-axis? Answer in units of in. column closed at one end that will respond to a tuning fork of frequency 183 Hz? Answer in units of cm.
6. A wave is described by y = 0.020 8 sin(kx - wt), where k = 2.22 rad/m, w = 3.66 rad/s, x and y are in meters, and t is in seconds. (a) Determine the amplitude of the wave. (b) Determine the wavelength of the wave. (c) Determine the frequency of the wave. (d) Determine the speed of the wave. 7. When a particular wire is vibrating with a frequency of 3.00 Hz, a transverse wave of wavelength 64.0 cm is produced. Determine the...
A wave is described by y 0.020 2 sin(kx wt), where k 2.18 rad/m, w 3.60 rad/s, x and y are in meters, and t is in seconds. (a) Determine the amplitude of the wave. m (b) Determine the wavelength of the wave (c) Determine the frequency of the wave. Hz (d) Determine the speed of the wave. m/s
1. Two waves are traveling along a rope. The individual waves are de- scribed by hi(t, x) = h2(t, x) = 0.3 cos(8x – 4t) 0.3 cos(7.6x - 3.8t) (a) Write the superposition hi + h, in the form h(t, x) = Acos (į Aku - Awt) cos (Kx – wt) (b) What is the amplitude A of the combined wave? (c) What is the phase velocity of the combined wave? (d) What is the group velocity All of the...
These two waves travel along the same string: y1 = (4.10 mm) sin(1.51?x - 370?t) y2 = (5.53 mm) sin(1.51?x - 370?t + 0.867?rad). What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 5.11 mm is also to be sent along the string in the same direction as the first two waves, what should be its phase angle in order to maximize the amplitude...
Two identical traveling waves, moving in the same direction, are out of phase by π/1 rad. What is the amplitude of the resultant wave in terms of the common amplitude ym of the two combining waves?
Two waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelength of 2 cm and an amplitude of 0.02 m. What is the amplitude of the resultant wave if the original wave differ in phase by: π/6 π/3 What is the phase difference between the waves if the amplitude of the resultant wave is 0.02 m, the same as the original wave?
These two waves travel along the same string: y1 = (3.73 mm) sin(1.62πx - 350πt) y2 = (5.43 mm) sin(1.62πx - 350πt + 0.768πrad). What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c) If a third wave of amplitude 5.18 mm is also to be sent along the string in the same direction as the first two waves, what should be its phase angle in order to maximize the amplitude...
A standing wave results from the sum of two transverse traveling waves given by y1 = ymcos(kx - ωt) and y2 = ymcos(kx + ωt) where ym = 0.047 m, k = 3.2 rad/m, and ω = 12 rad/s. (a) What is the smallest positive value of x that corresponds to a node? Beginning at t = 0, what is the value of the (b) first, (c) second, and (d) third time the particle at x = 0 has zero...