Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 30, Problem 45P
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The proof that any function of form
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An E&M wave has an e-field given by E(x,t) = -(9.90 V/m)kcos(ky+wt) and its wavelength is known to be 20 micrometers. Which of the following is correct for B(x,t) and the direction of propagation? (c=3x108 m/s)
Show that p(t, x) = A sin (ωt − kx + φ) satisfies the wave equation.
Two sinusoidal waves of wavelength λ = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the right with same velocity v = 60 m/s. The resultant wave function y_res (x,t) will have the form:
Chapter 30 Solutions
Physics for Scientists and Engineers
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- Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a standing wave. The linear mass density of the string is =0.075 kg/m and the tension in the string is FT=5.00 N. The time interval between instances of total destructive interference is t=0.13 s. What is the wavelength of the waves?arrow_forwardA light wave traveling in a vacuum has a propagation constant of 1.256 x 107 m-1 . What is the angular freequency of the wave? (Assume that the speed of light is 3.00 x108 m/s.) a. 300 rad/s b. 3.77 x 1014 rad/s c. 3.00 x 108 rad/s d. 3.00 x 1015 rad/s e. 3.77 x 1015 rad/sarrow_forwardA travelling wave is represented by the function : y (x,t) = 0.009 m sin ( 1.2 m -1 x - 5.0 s-1 t) Find the following : a.) Amplitude b.) Wave number C.)Wavelength d.) Angular frequency e.) Frequency f.) Wave speed A travelling sinusoidal wave has this equation : y(x,t) = 0.0450 m sin (25.12 m-1 x - 37.68 s-1 t - 0.523) a.) Amplitude B.) Wave number C.) Wavelength d.) Angular frequency E.) Frequency f.) Phase anglearrow_forward
- 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.arrow_forwardTwo sinusoidal waves travelling in the same direction with the same amplitude, wavelength, and speed, interfere with each other to give the resultant wave: y_res (x,t) = 2 cm sin(4πx-60πt+π/3). The amplitude of the individual waves generating this wave is:arrow_forwardTwo waves of amplitudes 4.2 m and 8.4 m, angular frequencies 235.5 rad/s, propagation constants 0.628 rad/m having phase difference 180 degree interfere with each other. The frequency of each wave is___________ a. 37.5 Hz b. 100 Hz c. 150 Hz d. 5 Hzarrow_forward
- Two sinusoidal waves of wavelength λ = 2/3 m and amplitude A = 6 cm and differing with their phase constant, are travelling to the left with same velocity v = 50 m/s. The resultant wave function y_res (x,t) will have the form: y_res (x,t) = 12(cm) cos(φ/2) sin(150πx+3πt+φ/2). y_res (x,t) = 12(cm) cos(φ/2) sin(3πx+150πt+φ/2). y_res (x,t) = 12(cm) cos(φ/2) sin(3πx-150πt+φ/2). y_res (x,t) = 12(cm) cos(φ/2) sin(3πx-180πt+φ/2). y_res (x,t) = 12(cm) cos(φ/2) sin(150πx-3πt+φ/2).arrow_forwardConsider a transverse periodic (sinusoidal) wave passing through a very long string of mass density 0.250 kg/m. The wave function for this wave is found to be: y (x,t) = (0.125 m) cos [(1.10 rad/m) x - (15.0 rad/s) t] From the equation find the following quantites; 1. Wave amplitude 2. Wave number 3. Angular frequency 4. Wavelength 5. Period 6. Frequencyarrow_forwardA traveling wave along the x-axis is given by the following wave functionψ(x, t) = 3.5 cos(1.5x - 8.6t + 0.46). Calculate the phase constant in radians.arrow_forward
- A travelling sinusoidal wave has this equation : y(x,t) = 0.0450 m sin (25.12 m-1 x - 37.68 s-1 t - 0.523) a.) Amplitude B.) Wave number C.) Wavelength d.) Angular frequency E.) Frequency f.) Phase anglearrow_forwardExample 14-8 depicts the following scenario. Two people relaxing on a deck listen to a songbird sing. One person, only 1.66 m from the bird, hears the sound with an intensity of 2.86×10−6 W/m^2. A bird-watcher is hoping to add the white-throated sparrow to her "life list" of species. How far could she be from the bird described in example 14-8 and still be able to hear it? Assume no reflections or absorption of the sparrow's sound.arrow_forwardTwo identical sinusoidal waves with wavelengths of 1.5 m travel in the same direction at a speed of 20 m/s. If the two waves originate from the same starting point, but with time delay ∆t between them, and with resultant amplitude A_resultant = √3 A then ∆t will be equal to: 0.00625 sec 0.0125 sec 0.025 sec 0.01 sec 0.005 secarrow_forward
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