Standing Waves and Resonance in Fixed-End Transverse String Vibration

In summary, the conversation discusses the concept of standing waves on a string fixed at both ends. It is mentioned that a standing wave is produced when a wave is summed with its reflection at any frequency. The question is raised whether the standing wave resonates only when there are nodes at each end. Further clarification is given that it could also be antinodes for a sound wave and an open pipe. The conversation also refers to a helpful video for understanding the topic. The idea of resonating is discussed in relation to the string absorbing energy from an external source oscillating at one of its natural frequencies.
  • #1
ofeyrpf
30
0
Hi,
Considering a transverse wave on a string fixed at both ends... I understand that a wave summed with its reflection will produce a standing wave at any frequency.
Is it correct that this standing wave is resonating only when that standing wave has nodes at each end?
(Well not necessarily node, could be antinodes for a sound way and an open pipe.)
Any help would be greatly appreciated,
Thanks,
Shane
 
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  • #2
This video is good for a start:
 
  • #3
If the string is fixed at both ends, it's bound to have nodes at both ends. That quantises the frequencies at which it can vibrate. I wouldn't talk about resonating unless you really mean that the string is absorbing energy from an external 'driver' (such as a tuning fork) which is oscillating at one of the string's natural frequencies.
 

1. What is a standing wave?

A standing wave is a type of wave that forms when two waves with the same amplitude and frequency travel in opposite directions and interfere with each other. The points where the two waves cancel each other out are called nodes, while the points where the waves reinforce each other are called antinodes. This results in a pattern of stationary nodes and antinodes that do not appear to move.

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

A traveling wave moves through a medium, carrying energy from one point to another. In contrast, a standing wave does not appear to move through the medium, but rather stays in one place. Additionally, a traveling wave can have varying amplitudes and frequencies, while a standing wave has a fixed amplitude and frequency determined by the two interfering waves.

3. What is resonance in relation to standing waves?

Resonance occurs when an object or system is forced to vibrate at its natural frequency. In the case of standing waves, resonance is achieved when the frequency of the standing wave matches the natural frequency of the medium it is traveling through. This results in an amplification of the standing wave's amplitude.

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

Standing waves and resonance have various applications in fields such as acoustics, engineering, and physics. Some examples include musical instruments such as stringed instruments and wind instruments, where standing waves are responsible for producing specific notes. Resonance is also utilized in sonar technology, where sound waves are used to detect objects underwater, and in seismology, where standing waves can help scientists study the properties of the Earth's interior.

5. How can standing waves be manipulated or controlled?

Standing waves can be manipulated by changing the frequency or wavelength of the interfering waves, which can be achieved by altering the properties of the medium they are traveling through. For example, the length or tension of a string can be adjusted to change the frequency of standing waves in a musical instrument. Additionally, standing waves can be controlled by using dampening materials to reduce their amplitude and prevent resonance from occurring.

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