# Harmonics Problem: Frequency Matching of Strings A and B

• bearhug
In summary: So, in summary, if the 2nd harmonic of B matches the fundamental of A, then B is shorter than A. If the 3rd harmonic of B matches the fundamental of A, then B is shorter than A. If the 4th harmonic of B matches the fundamental of A, then B is shorter than A.
bearhug
String A is stretched between two clamps separated by distance L. String B, with the same linear density and under the same tension (i.e., having the same wave velocity) as String A, is stretched between two other clamps separated by distance 4L. Consider the first 8 harmonics of string B. For which, if any, of these 8 harmonics does the frequency matched the frequency of the following harmonics of string A:
(a)First? 4
(b)Second?
(c)Third? 0

For some reason I'm thinking that there aren't any equations to use for this sort of problem but that it is more visual. I have the first answer right because I figured that once string A is stretched to 4L it's Tension is 4T which makes it's frequencies 4xs faster than String B. However for the second harmonic I'm having a hard time figuring out, unless the frequencies slow down. Am I approaching this the right way?

I don't think A is stretched to 4T. The way I read the problem statement the two strings have the same tension, but B is 4 times as long. So which harmonic of B will have the same frequency as the fundamental of A?

EDIT -- I had A & B backwards. Fixed it. B is 4x as long as A.

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<< Direct answer deleted by berkeman -- please don't post the answer. Just help guide the OP to the answer with hints. >>

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bearhug -- just think about how the fundamental and harmonics look on a plucked string. The fundamental has a how many sine periods (or sub-periods) between the string ends? The 2nd harmonic how many full sine-periods between the ends? The 4th harmonic has how many full sine periods between the two ends? etc...

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Quick question, do these strings slow down at all or do I assume they are going at a constant rate. Also can the answer be a fraction?

Any real string will have its oscillations slow down at some damping rate, but that affects the amplitude, not the frequency. Otherwise guitars would sound pretty strange...

The way I read the problem, they want to know which harmonics of the longer string match the fundamental of the shorter string. I could be reading it incorrectly, however.

## 1. What is the Harmonics Problem?

The Harmonics Problem is a physics phenomenon that occurs when two strings with different frequencies are played together and produce a beating or pulsating sound. This is caused by the frequencies of the two strings not being in sync with each other.

## 2. How is the frequency matching of strings A and B achieved?

Frequency matching of strings A and B can be achieved by adjusting the tension or length of the strings until the frequencies of both strings are in sync. This can also be achieved by using a tuner to accurately tune both strings to the same frequency.

## 3. What causes the beating sound in the harmonics problem?

The beating sound in the harmonics problem is caused by the interference of the two frequencies of strings A and B. When two frequencies are close but not identical, they create a pulsating sound due to the overlapping of their sound waves.

## 4. Can the Harmonics Problem be solved?

Yes, the Harmonics Problem can be solved by adjusting the tension or length of the strings or by using a tuner to accurately tune both strings to the same frequency. With proper adjustments, the two strings will be in sync and the beating sound will disappear.

## 5. Is the Harmonics Problem only applicable to strings?

No, the harmonics problem can occur with any vibrating objects, such as air columns in musical instruments or electronic circuits. It is a common phenomenon in physics and can be observed in various contexts.

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