Concept explainers
(a)
To calculate:
(a)
Answer to Problem 46P
It is proved that
Explanation of Solution
Given:
The speed of the wave is
The speed of the wave is
Formula used:
Consideration:
This limit gives
Calculation:
Both the wave function and its first spatial derivative are continuous at
Let, the
Now, to expression for continuity of the two-wave function’s at
And
Or
The sine function is odd as it is symmetric about the origin. So,
Now, differentiate the wave functions with respect to
And
Now, express the continuity of the slopes of the two wave functions at
And
The cosine function is even as it is symmetric about the
Multiply the equation
Now to solving for,
Solve for
Now, put the equation (1) to get,
Solving for
Conclusion:
Hence, it is proved
(b)
To calculate:
(b)
Answer to Problem 46P
The identified equation is,
Explanation of Solution
Given:
The speed of the wave is
The speed of the wave is
Formula used:
Consideration:
This limit gives
Calculation:
To show the
In which,
After substituting the values in equation,
And then check to see if result equation is identified or not,
Therefore, identified equation is,
Conclusion:
Therefore, identified equation is
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Chapter 15 Solutions
Physics for Scientists and Engineers, Vol. 3
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