
Concept explainers
(a)
To Find:The maximum kinetic energy of the wire.
(a)

Explanation of Solution
Given:
Length of the wire,
Tension in the wire,
Mass of the wire,
At the midpoint, amplitude is
Formula Used:
Maximum kinetic energy of the wire can be obtained by:
Here, m is the mass,
Here, f is the frequency which can be obtained by:
Calculations:
Find the mass per unit length:
Now calculate the frequency of the vibrating wire in fundamental mode:
The angular frequency is:
Now substitute all the known values to find the maximum kinetic energy of the wire:
Conclusion:
Thus, the maximum kinetic energy of the wire is
(b)
To Find: The kinetic energy of the wire at the instant when transverse displacement is given by
(b)

Explanation of Solution
Given:
Length of the wire,
Tension in the wire,
Mass of the wire,
At the midpoint, amplitude is
Displacement,
Formula Used:
Wave equation of standing wave in fundamental mode:
Calculations:
Compare the given displacement and the wave equation:
Conclusion:
Thus, the kinetic energy at the given instant would be zero.
(c)
To Find: The value of x for which the average value of the kinetic energy per unit length is the greatest.
(c)

Explanation of Solution
Given:
Length of the wire,
Tension in the wire,
Mass of the wire,
At the midpoint, amplitude is
Displacement,
Formula Used:
Average value of kinetic energy per unit length:
Here,
Wave equation of standing wave in fundamental mode:
Calculations:
For maxima, equate the derivative with zero.
Conclusion:
Thus, the value of x for which the average value of the kinetic energy per unit length is the greatest is
(d)
To Find: The value of x for which the elastic potential energy per unit length has the maximum value.
(d)

Explanation of Solution
Given:
Length of the wire,
Tension in the wire,
Mass of the wire,
At the midpoint, amplitude is
Displacement,
Formula Used:
Average value of elastic potential energy per unit length:
Here,
Wave equation of standing wave in fundamental mode:
Calculations:
For maxima, equate the derivative with zero.
Conclusion:
Thus, the value of x for which the average value of the elastic potential energy per unit length is the greatest is at
Want to see more full solutions like this?
Chapter 16 Solutions
Physics for Scientists and Engineers
- Two conductors having net charges of +14.0 µC and -14.0 µC have a potential difference of 14.0 V between them. (a) Determine the capacitance of the system. F (b) What is the potential difference between the two conductors if the charges on each are increased to +196.0 µC and -196.0 µC? Varrow_forwardPlease see the attached image and answer the set of questions with proof.arrow_forwardHow, Please type the whole transcript correctly using comma and periods as needed. I have uploaded the picture of a video on YouTube. Thanks,arrow_forward
- A spectra is a graph that has amplitude on the Y-axis and frequency on the X-axis. A harmonic spectra simply draws a vertical line at each frequency that a harmonic would be produced. The height of the line indicates the amplitude at which that harmonic would be produced. If the Fo of a sound is 125 Hz, please sketch a spectra (amplitude on the Y axis, frequency on the X axis) of the harmonic series up to the 4th harmonic. Include actual values on Y and X axis.arrow_forwardSketch a sign wave depicting 3 seconds of wave activity for a 5 Hz tone.arrow_forwardSketch a sine wave depicting 3 seconds of wave activity for a 5 Hz tone.arrow_forward
- The drawing shows two long, straight wires that are suspended from the ceiling. The mass per unit length of each wire is 0.050 kg/m. Each of the four strings suspending the wires has a length of 1.2 m. When the wires carry identical currents in opposite directions, the angle between the strings holding the two wires is 20°. (a) Draw the free-body diagram showing the forces that act on the right wire with respect to the x axis. Account for each of the strings separately. (b) What is the current in each wire? 1.2 m 20° I -20° 1.2 marrow_forwardplease solve thisarrow_forwardplease solve everything in detailarrow_forward
- 6). What is the magnitude of the potential difference across the 20-02 resistor? 10 Ω 11 V - -Imm 20 Ω 10 Ω 5.00 10 Ω a. 3.2 V b. 7.8 V C. 11 V d. 5.0 V e. 8.6 Varrow_forward2). How much energy is stored in the 50-μF capacitor when Va - V₁ = 22V? 25 µF b 25 µF 50 µFarrow_forward9). A series RC circuit has a time constant of 1.0 s. The battery has a voltage of 50 V and the maximum current just after closing the switch is 500 mA. The capacitor is initially uncharged. What is the charge on the capacitor 2.0 s after the switch is closed? R 50 V a. 0.43 C b. 0 66 C c. 0.86 C d. 0.99 C Carrow_forward
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
- University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning





