Concept explainers
(a)
To calculate:
Calculate the wave speed and its direction.
(a)
Answer to Problem 41P
The wave speed is
Explanation of Solution
Given:
Wave function:
Formula used:
The speed of the wave is determined by:
Where,
Calculation:
The wave function
For wave travelling in
The wavelength, frequency and the period of the wave is determined from the
As the given wave function is,
And because of the sign in between the
The speed of the wave is,
Thus,
Conclusion:
Thus, the wave speed is
(b)
To calculate:
Calculate the wavelength, frequency and period of the wave.
(b)
Answer to Problem 41P
The wavelength
Explanation of Solution
Given:
Wave function:
Formula used:
The wavelength is determined by:
Where,
The period is determined by:
Where,
Calculation:
The wave function
For wave travelling in
The wavelength, frequency and the period of the wave is determined from the
The coefficient of the
Where,
Now, substitute the numerical values to evaluate
The coefficient of the
The period of the wave motion is the reciprocal of its frequency,
Conclusion:
Thus, the wavelength
(c)
To calculate:
Calculate the maximum speed of any point on the string.
(c)
Answer to Problem 41P
The maximum speed
Explanation of Solution
Given:
Wave function:
Formula used:
The max velocity is calculated as:
where,
Calculation:
To express and evaluate the maximum speed of any string segment is,
Conclusion:
Thus, the maximum speed
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Chapter 15 Solutions
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