Standing waves and resonance frequency

In summary, the conversation discusses standing waves on a string of length L and their relationship to the string's resonance frequencies. The link provided confirms that the frequencies mentioned are indeed the resonant frequencies of the string. There is a brief tangent about a user's icon, but the conversation primarily focuses on the main topic.
  • #1
Niles
1,866
0

Homework Statement


Hi all.

I have shown that standing waves occur on a string of length L (fastened at x=0 and x=L) for angular frequencies:

[tex]
\omega_n=n\frac{v\pi}{L}.
[/tex]

Are these frequencies the same as the strings resonance frequencies?

Thanks in advance.

Regards,
Niles.
 
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  • #3
Hmm, not really. I'm just wondering if the above frequencies are the resonant frequencies of the string.
 
  • #4
Yes. According to LowlyPion's link, standing waves are pretty much synonymous with a string's resonant modes.
 
  • #5
Redbelly98 said:
Yes. According to LowlyPion's link, standing waves are pretty much synonymous with a string's resonant modes.

Im going to highjack this thread and say that redbelly has the best icon of all time... I am not sure why but I am laughing hysterically at the sight of a bird wrapped in Christmas lights hahah
 
  • #6
Hmm, yeah.. I guess it does say indirectly.

Thanks to all.
 
  • #7
NBAJam100 said:
Im going to highjack this thread and say that redbelly has the best icon of all time...

Thanks!

Niles said:
Thanks to all.

You're welcome.
 

1. What is a standing wave?

A standing wave is a type of wave that appears to be standing still, rather than moving through space. It is created by the interference of two waves traveling in opposite directions, which results in points of maximum and minimum amplitude that do not move.

2. How is a standing wave different from a traveling wave?

A traveling wave moves through space, carrying energy from one point to another. In contrast, a standing wave does not move through space, but rather appears to oscillate in place. Additionally, a traveling wave has a continuously changing amplitude and phase, while a standing wave has fixed points of maximum and minimum amplitude.

3. What is resonance frequency?

Resonance frequency is the frequency at which a system naturally vibrates or oscillates with the greatest amplitude. When the frequency of an external force matches the resonance frequency of a system, it can cause the system to vibrate with a larger amplitude, resulting in resonance.

4. How is resonance frequency related to standing waves?

Standing waves are created when two waves with the same frequency and amplitude interfere with each other. The points of maximum and minimum amplitude in a standing wave correspond to the nodes and antinodes of the wave, respectively. These nodes and antinodes have fixed locations and are determined by the resonance frequency of the system.

5. What are some real-world applications of standing waves and resonance frequency?

Standing waves and resonance frequency have various applications in science and technology, including musical instruments, sound systems, and radio and television communication. They are also used in medical imaging techniques, such as ultrasound and MRI, to produce images of internal body structures.

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