Concept explainers
(a)
To Find:The derivative of wave speed on a string with respect to the tension.
(a)
Explanation of Solution
Given:
Differentials
Formula used:
The speed of the transverse wave is given by
Where,
Calculation:
For differentiating the expression with respect to
For evaluating the
Now, to separate the variables to obtain
Conclusion:
Thus, derivative of the speed of the wave on a string with respect to the tension is
(b)
To Calculate:The tension that must be changed to increase the speed to
(b)
Answer to Problem 33P
The tension that must be changed to increase the speed to
Explanation of Solution
Given:
Speed of the wave
Tension
The speed is increased to 312 m/s.
Formula used:
Calculation:
To estimate how much tension must be changed to increase the speed of the wave to
Approximate the
Put the numerical values to get
Conclusion:
Thus, the tension that must be changed to increase the speed to
(c)
To Calculate:
(c)
Answer to Problem 33P
The value of the
Explanation of Solution
Given:
Speed of the wave
Tension
Formula used:
Wave speed of a transverse wave is given by:
Calculation:
The exact value for
Express the wave speeds for the two tensions
After that dividing the second equation by the first one, it simply yields:
Put the value of
Put the numerical values to evaluate
Now, to find the percent error between the exact and approximate values for
Conclusion:
Thus, the value of the
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Chapter 15 Solutions
Physics for Scientists and Engineers
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