Concept explainers
(a)
The difference between two waves on a string given by
(a)
Answer to Problem 1PQ
The wave 1 propagates in
Explanation of Solution
Write the expression for a wave travelling along
Here,
Write the expression for a wave travelling along
Here,
Write the given waves in string.
Conclusion:
Consider the mathematical expression
Rearrange equation (III) using above equation and change wave in equation (III) into sign wave.
The above equation represents same cosine wave in terms of sinusoidal wave with initial phase of
Now comparing above equation with equation (I) it is clear that equation (V) and (I) are matching. Thus, the wave is travelling along
Consider the mathematic expression
Rearrange equation (IV) using above equation and change the wave in equation (IV) into sign wave.
The above equation represents same cosine wave in terms of sinusoidal wave with initial phase of
Now comparing above equation with equation (II) it is clear that the equations (VI) and (II) are matching. Thus, the wave is travelling along
Therefore, the wave 1 propagates in
(b)
The wave that results on this string.
(b)
Answer to Problem 1PQ
The wave that results on this string is
Explanation of Solution
Rewrite equations (III) and (IV).
When these waves moves in medium with one along
Write the expression for the resultant of these waves.
Conclusion:
Substitute (III) and (IV) in (VII) to get resultant of two waves.
Use trigonometric equation,
Therefore, the wave that results on this string is
(c)
The amplitude of resultant wave.
(c)
Answer to Problem 1PQ
The amplitude of resultant wave is
Explanation of Solution
The resultant standing wave is
Write the standard equation of a standing wave produced from waves given in (I) and (II).
In above equation the term in square bracket
Conclusion:
Comparing above two equations, it is clear that
Therefore, the amplitude of resultant wave is
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Chapter 18 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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