Speed of wave on guitar string

[toothpaste666]

Homework Statement

A 65-cm guitar string is fixed at both ends. In the frequency range between 1.0 and 2.0 kHz, the string is found to resonate only at frequencies 1.2, 1.5, and
1.8kHz .

What is the speed of traveling waves on this string?

Homework Equations

f = v/2l

The Attempt at a Solution

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Each one of these is a multiple of .3 so i think that is the fundamental frequency. Then I use f=v/2l or
v=2lf
v= 2 * .65 * .3
v = .39

but i did it wrong. can someone help please

 

[jz92wjaz]

Check your units. You need to convert kHz to Hz in order to come up with a velocity in m/s.

 

[voko]

Homework Equations

f = v/2l

What does "l" mean in that equation? And where does the equation come from?

 

[toothpaste666]

Check your units. You need to convert kHz to Hz in order to come up with a velocity in m/s.

oh wow can't believe i missed that. thank you

 

[HalfLostAndSearching]

I would like to clarify a few things. First, it is important to note that the frequency at which a guitar string resonates is determined by its length, tension, and mass per unit length. Therefore, the given information about the frequency range and resonant frequencies cannot be used to directly calculate the speed of waves on the string.

To calculate the speed of waves on the string, we need to use the equation v = √(T/μ), where T is the tension in the string and μ is the mass per unit length. However, without knowing the tension and mass per unit length of the string, it is not possible to accurately determine the speed of waves on the string.

Additionally, the equation f = v/2l is used to calculate the fundamental frequency of a string, not the speed of waves. Therefore, it cannot be used to solve this problem.

In order to accurately determine the speed of waves on the guitar string, we would need to know the tension and mass per unit length of the string. These can be measured experimentally or provided in the problem statement. Without this information, the speed of waves on the string cannot be determined.