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# question 7 - Phys 211 J Jacobs Fall 2008 Homework 16...

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Phys 211 Fall 2008 J. Jacobs Homework 16 Solutions HRW 16.8 The equation of a transverse wave traveling along a very long string is y = 6 . 0 sin (0 . 020 πx + 4 . 0 πt ), where x and y are expressed in centimeters and t is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of propagation of the wave, and (f) the maximum transverse speed of a particle in the string. (g) What is the transverse displacement at x = 3 . 5 cm when t = 0 . 26 s? We are given the displacement as a function of position and time: y = 6 . 0 sin (0 . 020 πx + 4 . 0 πt ) with x and y in cm and t in s. Comparing this to: y = A sin ( kx ± ωt ) we have: A = 6 . 0 cm, k = 0 . 020 π cm - 1 , and ω = 4 . 0 π s - 1 . (a) Amplitude: A = 6 . 0 cm , (b) Wavelength: λ = 2 π k = 100 cm = 1 . 00 m , (c) Frequency: f = ω 2 π = 2 . 0 Hz (d) Speed: v = ω k = 2 . 00 m / s , (e) Propagates in the - x direction, (f) Particle speed: v max = = 0 . 753 m / s (g) y (3 . 5 cm , 0 . 26 s) = 6 . 0 sin [0 . 020 π (3 . 5) + 4 . 0 π (0 . 26)] = - 2 . 03 cm HRW 16.71 A sinusoidal transverse wave traveling in the negative direction of an x axis has an amplitude of 1.00 cm, a frequency of 550 Hz, and a speed of 330 m/s. If the wave equation is of the form y ( x, t ) = y m sin ( kx ± ωt ), what are (a) y m , (b) ω , (c) k , and (d) the correct choice of sign in fromt of ω ? We are given the amplitude, A = 1 . 00 cm, the frequency, f = 550 Hz, the speed v = 330 m / s, and the form of the displacement, y = A sin ( kx ± ωt ). (a) Amplitude: A = 1 . 00 cm = 0 . 010 m (b) Angular frequency: ω = 2 πf = 1100 π s - 1 (c) Wavenumber: k = ω v = 3 . 33 π m - 1 (d) + sign for propagation in - x direction. HRW 16.70 A sinusoidal transverse wave traveling in the positive direction of an x axis has an amplitude of 2.0 cm, a wavelength of 10 cm, and a frequency of 400 Hz. If the wave equation is of the form y ( x, t ) = y m sin ( kx ± ωt ), what are (a) y m , (b) k , (c) ω , and (d) the correct choice of sign in fromt of ω ? What are (e) the maximum transverse speed of a point on the cord and (f) the speed of the wave? We are given the amplitude, A = 2 . 0 cm, the wavelength, λ = 10 cm = 0 . 10 m, the frequency f = 400 Hz, and the form of the displacement, y = A sin ( kx ± ωt ). (a) Amplitude: A = 2 . 0 cm (b) Wavenumber: k = 2 π λ = 0 . 20 π m - 1 (c) Angular frequency: ω = 2 πf = 800 π s - 1 (d) - sign for propagation in + x direction.

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question 7 - Phys 211 J Jacobs Fall 2008 Homework 16...

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