Concept explainers
(a)
The sinusoidal wave at time
(a)
Answer to Problem 12P
The sinusoidal wave at time
.
Explanation of Solution
The wave is traveling in the negative
The general expression for the wave function of a sinusoidal wave is,
Here,
Substitute
At
Substitute
At
The graph for the above equation (III) is shown below.
Figure I
Conclusion:
Therefore, the sinusoidal wave at time
(b)
The angular wave number.
(b)
Answer to Problem 12P
The angular wave number is
Explanation of Solution
Formula to calculate the angular wave number is,
Substitute
Conclusion:
Therefore, the angular wave number is
(c)
The period of the wave from frequency.
(c)
Answer to Problem 12P
The period of the wave from frequency is
Explanation of Solution
Formula to calculate the period is,
Substitute
Conclusion:
Therefore, the period of the wave from frequency is
(d)
The angular frequency of the wave.
(d)
Answer to Problem 12P
The angular frequency of the wave is
Explanation of Solution
Formula to calculate the angular frequency is,
Substitute
Conclusion:
Therefore, the angular frequency of the wave is
(e)
The speed of the wave.
(e)
Answer to Problem 12P
The speed of the wave is
Explanation of Solution
Formula to calculate the speed of the wave is,
Substitute
Conclusion:
Therefore, the speed of the wave is
(f)
The phase constant
(f)
Answer to Problem 12P
The phase constant
Explanation of Solution
As calculated in part (a), the phase constant is,
Conclusion:
Therefore, the phase constant
(g)
The expression for the wave function
(g)
Answer to Problem 12P
The expression for the wave function is,
Explanation of Solution
The expression for the wave function from equation (II) is,
Or it may be written as,
Here,
Conclusion:
Therefore, the expression for the wave function
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Chapter 13 Solutions
Principles of Physics
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