Fundamental Frequency of Vibrating String: From 256Hz to ?Hz

In summary, the fundamental frequency of a vibrating string is the lowest frequency at which the string can vibrate and produce a standing wave. It can be calculated using the formula f = v/2L, where f is the frequency in Hertz, v is the speed of the wave in meters per second, and L is the length of the string in meters. The fundamental frequency is inversely proportional to the length of the string and can be changed by altering its length, tension, or mass. The range of fundamental frequencies for a vibrating string is infinite, but for a typical guitar string, it is usually between 82 Hz to 1,186 Hz.
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Homework Statement


The fundamental frequency of a vibrating stretched string of length 1.0m is 256Hz.When the string is shortened to 0.4m with the same tension,the fundamental frequency now become
how many Hz?


Homework Equations





The Attempt at a Solution

 
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No attempt, no help!
 
  • #3
attempt using basic equations. check your theory book once again.
 

1. What is the fundamental frequency of a vibrating string?

The fundamental frequency of a vibrating string is the lowest frequency at which the string can vibrate and produce a standing wave. It is also known as the first harmonic or the fundamental tone.

2. How is the fundamental frequency of a vibrating string calculated?

The fundamental frequency of a vibrating string can be calculated using the formula f = v/2L, where f is the frequency in Hertz, v is the speed of the wave in meters per second, and L is the length of the string in meters.

3. What is the relationship between the length of a string and its fundamental frequency?

The fundamental frequency of a vibrating string is inversely proportional to the length of the string. This means that as the length of the string increases, the fundamental frequency decreases, and vice versa.

4. Can the fundamental frequency of a vibrating string be changed?

Yes, the fundamental frequency of a vibrating string can be changed by altering its length, tension, or mass. For example, tightening the string or shortening its length will increase the fundamental frequency, while loosening the string or lengthening it will decrease the fundamental frequency.

5. What is the range of fundamental frequencies for a vibrating string?

The range of fundamental frequencies for a vibrating string is infinite. However, for a typical guitar string, the range is usually between 82 Hz to 1,186 Hz, with the lowest string producing the lowest fundamental frequency and the highest string producing the highest fundamental frequency.

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