Concept explainers
(a)
The wavelength of the wave.
(a)
Answer to Problem 15PQ
The wavelength of the wave is
Explanation of Solution
Write the equation for wave function.
Here,
Compare the given equation to the Equation (17.4) and match the terms.
Here,
Write the expression from the relation between wavelength and wave number (Refer equation 17.5).
Here,
Rearrange the equation (III) for
Conclusion:
Substitute
Therefore, the wavelength of the wave is
(b)
The time period of the wave.
(b)
Answer to Problem 15PQ
The time period of the wave is
Explanation of Solution
Write the relation between
Here,
Conclusion:
Substitute
Therefore, the time period of the wave is
(c)
The speed of the wave.
(c)
Answer to Problem 15PQ
The speed of the wave is
Explanation of Solution
Write the equation for wave speed (Refer Equation 17.8).
Conclusion:
Substitute
Therefore, the speed of the wave is
(d)
The transverse velocity of a rope element.
(d)
Answer to Problem 15PQ
The transverse velocity of a rope element is
Explanation of Solution
Write the derivative form of transverse velocity at the rate of change of the y position in time.
Substitute equation (I) in the equation (VII) and differentiae it.
Conclusion:
Substitute
Write the velocity as a vector form.
Therefore, the transverse velocity of a rope element is
(e)
The transverse acceleration of a rope element.
(e)
Answer to Problem 15PQ
The transverse acceleration of a rope element is
Explanation of Solution
Write the derivative form of transverse acceleration at the rate of change of the velocity in time.
Substitute equation (VIII) in the equation (IX) and differentiae it.
Conclusion:
Substitute
Write the acceleration as a vector form.
Therefore, the acceleration of a rope element is
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Chapter 17 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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