Homework Answers
Answer : (a) Angular frequency is different, wavelength is different since wave number is different.
Amplitude is same, direction of motion is same, speed is same.
For (b) and (c) please find attached the picture.
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Two waves in the same medium are given by yix, t)3.8 sin(9.0x 3.4t) and y2(x, t)-3.8...
These two waves travel along the same string: y1 = (4.10 mm) sin(1.51?x - 370?t) y2...
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 waves, yı = (2.9 mm) sin [(22.1 rad /m)x – (540 rad/s)t] and y2 =...
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These two waves travel along the same string: y1 = (3.73 mm) sin(1.62πx - 350πt) y2...
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...
Four waves are to be sent along the same string, in the same direction: y1(x, t)...
Four waves are to be sent along the same string, in the same direction: y1(x, t) = (5.40 mm) sin(2πx - 410πt + 0.22π) y2(x, t) = (5.40 mm) sin(2πx - 410πt + 0.86π) y3(x, t) = (5.40 mm) sin(2πx - 410πt + 1.22π) y4(x, t) = (5.40 mm) sin(2πx - 410πt + 1.86π). What is the amplitude of the resultant wave?
Two traveling sinusoidal waves are described by the wave functions y1 = 4.80 sin [π(4.10x −...
Two traveling sinusoidal waves are described by the wave functions y1 = 4.80 sin [π(4.10x − 1125t)] y2 = 4.80 sin [π(4.10x − 1125t − 0.250)] where x, y1, and y2 are in meters and t is in seconds. (a) What is the amplitude of the resultant wave function y1 + y2?
no 1 and 2 Homework 3A: Standing Waves 1. Two waves propagate in one direction on...
no 1 and 2
Homework 3A: Standing Waves 1. Two waves propagate in one direction on a stretched rope. The frequency of the waves is 120 Hz. Both have the same amplitude of 4 cm and wavelength of 0.04 m. (a) Determine the amplitude of the resultant wave if the two original waves differ in phase by Tm/3? (b) What is the phase difference between the two waves if the amplitude of the resultant wave is 0.05 cm? 2. Two...
Chapter 16, Problem 037 GO These two waves travel along the same string: Y-(3.82 mm) sin(1.96x430)...
Chapter 16, Problem 037 GO These two waves travel along the same string: Y-(3.82 mm) sin(1.96x430) Y2 = (5.64 mm) sin(1.96x430 +0.780xrad), 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 4.54 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 of the...
A cos(kx - wt) and y2 = A cos(kx - wt - 6) represent two waves...
A cos(kx - wt) and y2 = A cos(kx - wt - 6) represent two waves traveling in the same direction with the same amplitude A, frequency w, and wave number k, but with a phase difference . Here, A = 14.0 m, w = 3.95 s1, and k 15.5 m-1 y, (a) Write the expression for the resultant of the two waves using the numerical values given above for A, w, and k. Do not enter units for the...
A wave is modeled by the wave function 2Tt y(x, t) (0.30 m) sin 4.50 7m(x+18.00t...
A wave is modeled by the wave function 2Tt y(x, t) (0.30 m) sin 4.50 7m(x+18.00t (A) Determine the wave's (a) amplitude; (b) wavelength; (c) propagation speed (d) frequency (e) direction of propagation (B) An element of the string is located at x 2.25 m (a) Show that the motion of this element is a simple harmonic motion with a transverse displacement of the form y(t) Acos ( t + ф). (b) Determine the phase constant φ (c) Give its...
Two waves on one string are described by the wave functions y,-2.0 cos(3.5x-1.9t) Y2 = 3.5...
Two waves on one string are described by the wave functions y,-2.0 cos(3.5x-1.9t) Y2 = 3.5 sin(4.5x-1.5t) where x and y are in centimeters and t is in seconds. Find the superposition of the waves i 2 at the following points. (Remember that the arguments of the trigonometric functions are in radians.) (a) x = 1.00, t = 1.00 cm (b) x-1.00, t = 0.500 cm (c) x = 0.500, t = 0 cm
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?...
no 1 and 2
Homework 3A: Standing Waves 1. Two waves propagate in one direction on a stretched rope. The frequency of the waves is 120 Hz. Both have the same amplitude of 4 cm and wavelength of 0.04 m. (a) Determine the amplitude of the resultant wave if the two original waves differ in phase by Tm/3? (b) What is the phase difference between the two waves if the amplitude of the resultant wave is 0.05 cm? 2. Two...
Chapter 16, Problem 037 GO These two waves travel along the same string: Y-(3.82 mm) sin(1.96x430) Y2 = (5.64 mm) sin(1.96x430 +0.780xrad), 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 4.54 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 of the...
A cos(kx - wt) and y2 = A cos(kx - wt - 6) represent two waves traveling in the same direction with the same amplitude A, frequency w, and wave number k, but with a phase difference . Here, A = 14.0 m, w = 3.95 s1, and k 15.5 m-1 y, (a) Write the expression for the resultant of the two waves using the numerical values given above for A, w, and k. Do not enter units for the...
A wave is modeled by the wave function 2Tt y(x, t) (0.30 m) sin 4.50 7m(x+18.00t (A) Determine the wave's (a) amplitude; (b) wavelength; (c) propagation speed (d) frequency (e) direction of propagation (B) An element of the string is located at x 2.25 m (a) Show that the motion of this element is a simple harmonic motion with a transverse displacement of the form y(t) Acos ( t + ф). (b) Determine the phase constant φ (c) Give its...
Two waves on one string are described by the wave functions y,-2.0 cos(3.5x-1.9t) Y2 = 3.5 sin(4.5x-1.5t) where x and y are in centimeters and t is in seconds. Find the superposition of the waves i 2 at the following points. (Remember that the arguments of the trigonometric functions are in radians.) (a) x = 1.00, t = 1.00 cm (b) x-1.00, t = 0.500 cm (c) x = 0.500, t = 0 cm
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