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Concept explainers
(a)
The angular frequency of the wave.
(a)
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Answer to Problem 11P
The angular frequency of the wave is
Explanation of Solution
Write the expression for the angular frequency of the wave.
Here,
The wave function of the given wave.
Use the trigonometric relation
Comparing equation (I) and (III).
Write the expression for the speed of the wave.
Conclusion:
Substitute,
Therefore, the angular frequency of the wave is
(b)
The wave number of the wave.
(b)
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Answer to Problem 11P
The wave number of the wave is
Explanation of Solution
Write the expression wave number.
Here,
Write the expression for wavelength.
Conclusion:
Substitute,
Substitute,
Therefore, the wave number of the wave is
(c)
The wave function of the wave.
(c)
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Answer to Problem 11P
The wave function of the wave is
Explanation of Solution
Write the general expression for wave function of a wave moving in positive
Here,
Conclusion:
Substitute,
Therefore, the wave function of the wave is
(d)
Themaximum transverse speed of the wave.
(d)
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Answer to Problem 11P
Themaximum transverse speed of the wave is
Explanation of Solution
The derivate of vertical displacement gives the transverse speed of the wave.
Conclusion:
Substitute,
The maximum value of cos is 1. Therefore the maximum transverse speed is.
Therefore, the maximum transverse speed of the wave is
(e)
The maximum transverse acceleration of an element of the string.
(e)
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Answer to Problem 11P
The maximum transverse accelerationof an element of the string is
Explanation of Solution
The transverse accelerationwill be equal to the derivative of transverse speed with respect to time.
Write the expression for the transverse acceleration.
Conclusion:
Substitute,
The maximum value of sine is 1. Therefore the maximum transverse acceleration is.
Therefore, the maximum transverse acceleration of an element of the string is
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Chapter 16 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 9th + WebAssign Printed Access Card, Multi-Term
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- A standing wave is the result of superposition of two harmonic waves given by the equations y1 (x, t) = A sin(wt – kæ) and y2(x, t) = A sin(wt + kæ). The angular frequency is w = 37 rad/s and the k = 27 rad/m is the wave number. (a) Give an expression for the amplitude of standing wave. (b) Determine the frequency. (c) Determine the wavelength of the wavearrow_forwardProblem 4: A traveling wave along the x-axis is given by the following wave functionψ(x, t) = 3.6 cos(1.4x - 9.2t + 0.34),where x in meter, t in seconds, and ψ in meters. Read off the appropriate quantities for this wave function and find the following characteristics of this plane wave: Part (a) The amplitude in meters. Part (b) The frequency, in hertz. Part (c) The wavelength in meters. Part (d) The wave speed, in meters per second. Part (e) The phase constant in radians.arrow_forwardIn the arrangement shown in the figure, an object of mass m=5.9 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L2.0 m. When the vibrator is set to a frequency of 150 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord?arrow_forward
- The mathematical model for a wave on a tightly stretched wire is y(x, t) = 0.340 sin 12xt Злх + 4 where x and y are in meters, t is in seconds, and u of the wire is 86.0 g/m. (a) Calculate the average rate energy is conveyed along the wire. Enter a number. (b) What is the energy per cycle of the wave? Enter a number.arrow_forwardJust need to be shown parts (a) and (b) Problem 12: A guitar string of length L = 0.99 m is oriented along the x-direction and under a tension of T = 118 N. The string is made of steel which has a density of ρ = 7800 kg / m3. The radius of the string is r = 9.4 x 10-4 m. A transverse wave of amplitude A = 0.0020 m is formed on the string. Part (a) Calculate the mass per unit length μ of the guitar string in kg / m. Part (b) Calculate the velocity (in m/s) of a traveling transverse wave on the guitar string. Part (c) Assume a form y1 = A sin(α) for the transverse displacement of the string. Enter an expression for α of a transverse wave on a string traveling along the positive x-direction in terms of its wavenumber k, the position x, its angular frequency ω, and the time t? α = k x - ω t ✔ Correct! Part (d) Assume a form y2 = A sin(α) for the transverse displacement of the string. Write an expression for α of a transverse wave on a string traveling along the…arrow_forwardA transverse periodic wave travels to the left along a string. Their characteristics are: amplitude of 0.200 m, wavelength of 0.350 m and a frequency of 12.0 Hz. The position of a portion of the string at t = 0, x = 0 is y = -0.0300 m, and the element has a positive velocity at that location. Find an expression for the wave function that describes it in terms of cosines.arrow_forward
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