Resonance in String: Understanding Wave Interference According to Book

In summary, the author presents a simplified picture of a wave crest generated by a vibrating fork on a string, traveling to the right end and being reflected back. The author assumes that the first crest travels 2L distance without interference, but in reality, it interferes with the next crest just after traveling a distance L. The setup is both driven and damped, but the formula for frequency may not be accurate for this specific scenario.
  • #1
AdityaDev
527
33
according to book "...Let us look at a particular wave crest generated at the left end of the string by a fork. It travels to the right end of the string, is reflected back, and is reflected again at the fork.Now it interferes with the next wave..."
doubt: the fork keeps vibrating and keeps producing waves. so just after it is reflected from the right end, it will interfere with the next crest right? why didthe author assume the first crest traveled 2L distance without interference? wouldn't it interfere withe next frest just after it travels a distance L?
 
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  • #2
The author is presenting a simplified picture. You should realize that all parts of the "incoming wave" interfere with all parts of the "reflected wave" to produce the wave you actually see.

The setup described is both driven and damped - but you don't have the maths for that yet.
 
  • #3
Simon Bridge said:
The author is presenting a simplified picture. You should realize that all parts of the "incoming wave" interfere with all parts of the "reflected wave" to produce the wave you actually see.

The setup described is both driven and damped - but you don't have the maths for that yet.
So the formula ##f=\frac{n}{2l}\sqrt{\frac{T}{\mu}}## is wrong?
 
  • #4
Wrong for what purpose?
Context is everything.
 

FAQ: Resonance in String: Understanding Wave Interference According to Book

1. What is resonance in a string?

Resonance in a string refers to the phenomenon where a vibrating string produces a sound with a specific frequency and amplitude. This frequency is determined by the tension, length, and mass of the string, and is also affected by the surrounding air and any interference with other waves.

2. How does wave interference affect resonance in a string?

Wave interference occurs when two or more waves meet and interact with each other. In the case of resonance in a string, this can either enhance or cancel out the amplitude of the wave, resulting in a change in the overall sound produced by the string. This interference can also create harmonic frequencies that contribute to the overall sound.

3. What factors affect the resonance frequency of a string?

The resonance frequency of a string is affected by the tension, length, and mass of the string. The tension can be adjusted by tightening or loosening the string, while the length can be changed by pressing down on different frets on a guitar or changing the length of a string on a different instrument. The mass of the string can also be altered by using different types of strings or adding weight to the string.

4. What is the role of air in resonance of a string?

The surrounding air plays a crucial role in the resonance of a string. As the string vibrates, it creates compressions and rarefactions in the air, which we perceive as sound. The properties of the air, such as temperature and density, can also affect the speed of sound and the resulting resonance frequency.

5. How is resonance in a string used in musical instruments?

Resonance in a string is the basis for producing sound in many musical instruments such as guitars, violins, and pianos. By manipulating the tension, length, and mass of the strings, musicians can create different frequencies and amplitudes to produce a variety of notes and melodies. Techniques like plucking, bowing, or striking the strings also affect the resonance and sound produced by the instrument.

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