Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 15, Problem 44P
To determine
To Calculate: The power transported by the waves as a function of x.
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Let us assume we are using SI units (kg, m, s).
Consider the harmonic travelling wave
17
y(x, t) = = 12 cos(3x - 12πt).
Assume the above harmonic wave is a solution of the motion of a string with tension T = 1 Newton.
What is the string's density?p=
kg/m
What is its kinetic energy density?
What is its kinetic energy over one wavelength? Ek
What is its potential energy density?
What is its potential energy over one wavelength? Ey =
J/m
J/m
A wave is modeled by the wave function:
y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)]
1. Find the wavelength, wave number, wave velocity, period and wave frequency.
2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s and the amplitude is A= 1.3m
3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically.
4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results? Justify your answer. Is the material transported long wave displacement? If yes, how much material is transported over time interval from t = 0 to t = 5 s? Comment on your answer. We now consider two sound waves with different frequencies which have to the same amplitude. The wave functions of these waves are as follows:
y1 (t) = A sin (2πf1t)
y2 (t) = A sin (2πf2t)
5. Find the resultant wave function analytically.
6. Study how the resulting wave…
A wave is described by the following wave function,
y(x, t) = 0,06 sin (0,02πx - 4nt)
a) Find the wavelength, the period of the wave and the speed of
propagation of the wave.
b) Make a graph of the wave function v/s time and another of the
wave function v/s length of the medium, where
explicitly appreciate the amplitude, initial phase, wavelength and
period of the wave.
Chapter 15 Solutions
Physics for Scientists and Engineers
Ch. 15 - Prob. 1PCh. 15 - Prob. 2PCh. 15 - Prob. 3PCh. 15 - Prob. 4PCh. 15 - Prob. 5PCh. 15 - Prob. 6PCh. 15 - Prob. 7PCh. 15 - Prob. 8PCh. 15 - Prob. 9PCh. 15 - Prob. 10P
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