Conservation of energy in standing wave

In summary, a standing wave is formed by small transverse oscillations of a taught string between an oscillator and a fixed point. The frequency is adjusted to be resonant at the third harmonic, resulting in a much greater amplitude of the string's vibration compared to the oscillator. This does not violate the principle of conservation of energy, as the superposition of the displacements of the new and reflected waves is greater than that of the oscillator. Further research on resonance can be done using the provided links.
  • #1
Saxby
45
0

Homework Statement


A standing wave is produced by small transverse oscillations of one end of a taught string stretched between an oscillator and a fixed point. The frequency of oscillation is adjusted to be resonant at the third harmonic.

The amplitude of the string's viabration is very much greater than that of the oscillator.
(i) Does this violate the principle of conservation of energy?
(ii) Explain why

The Attempt at a Solution


I do not believe this would violate the conservation of energy.

I think that if a standing wave is formed the addition (via superposition) of the displacements of points on the new and reflected waves should be more than that of the oscillator.

Does that sound like a valid explanation?
 
Physics news on Phys.org
  • #2
Saxby said:

Homework Statement


A standing wave is produced by small transverse oscillations of one end of a taught string stretched between an oscillator and a fixed point. The frequency of oscillation is adjusted to be resonant at the third harmonic.

The amplitude of the string's viabration is very much greater than that of the oscillator.
(i) Does this violate the principle of conservation of energy?
(ii) Explain why

The Attempt at a Solution


I do not believe this would violate the conservation of energy.

I think that if a standing wave is formed the addition (via superposition) of the displacements of points on the new and reflected waves should be more than that of the oscillator.

Does that sound like a valid explanation?
'Sounds like a fair explanation to me. :approve: (Edit: As a matter of fact, that's about the most concise explanation I can think of. I'd give you full credit.)

But just for good measure, here are a couple of links on resonance, for further research.
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reson.html
http://en.wikipedia.org/wiki/Resonance
 
Last edited:
  • #3
I also asked my lecturer and he said it sounded ok, thanks for your reply :)
 

1. What is the conservation of energy in standing wave?

The conservation of energy in standing wave refers to the principle that energy cannot be created or destroyed, but can only be transformed from one form to another. In a standing wave, the total energy remains constant as it oscillates between potential energy and kinetic energy.

2. How is energy conserved in a standing wave?

In a standing wave, energy is conserved through the continuous exchange between potential and kinetic energy. As the wave oscillates between its maximum displacement and rest position, the potential energy is at its maximum while the kinetic energy is at its minimum. As the wave passes through the rest position, the potential energy is at its minimum while the kinetic energy is at its maximum. This exchange ensures that the total energy of the standing wave remains constant.

3. What factors affect the conservation of energy in standing wave?

The conservation of energy in standing wave is affected by the amplitude, frequency, and damping of the wave. An increase in amplitude or frequency leads to an increase in the potential and kinetic energy, while damping causes a decrease in energy. Additionally, the medium through which the wave travels can also affect energy conservation.

4. How does the conservation of energy in standing wave relate to real-life applications?

The conservation of energy in standing wave has many real-life applications, such as in musical instruments. For example, the energy of a string in a guitar is conserved as it vibrates between its maximum displacement and rest position, producing different frequencies and thus, different notes. Additionally, this principle is also important in understanding and predicting earthquake behavior and in the development of renewable energy technologies.

5. Is the conservation of energy in standing wave a universal principle?

Yes, the conservation of energy in standing wave is a universal principle that applies to all types of waves, including sound waves, electromagnetic waves, and water waves. It is a fundamental concept in physics and is essential in understanding the behavior of waves in various systems and applications.

Similar threads

Length of string in a standing wave
    • Introductory Physics Homework Help
Replies
19
Views
327
Understanding Standing Waves in Open Tubes
    • Introductory Physics Homework Help
Replies
1
Views
888
How Do You Calculate the Energy of a Standing Wave?
    • Introductory Physics Homework Help
Replies
21
Views
2K
Waves and vibrations on a string
    • Introductory Physics Homework Help
Replies
2
Views
854
Waves on a String -- Minimizing reflections from the far end (ring on a bar)
    • Introductory Physics Homework Help
Replies
1
Views
961
Standing Wave Period for Third Harmonic Oscillation
    • Introductory Physics Homework Help
Replies
8
Views
1K
Wave equation, wavelenght not given
    • Introductory Physics Homework Help
Replies
6
Views
1K
I Let a standing wave of length L go, get traveling wave of length 2L?
    • Mechanics
Replies
11
Views
813
New wave after superposition (interference)
    • Introductory Physics Homework Help
Replies
4
Views
1K
B Potential energy in standing wave compared to traveling wave
    • Classical Physics
Replies
1
Views
765

Hot Threads

Recent Insights

Back
Top