# What Is the Speed of Waves on a Guitar String?

• toothpaste666
In summary, the content discusses a problem involving a 65-cm guitar string that is fixed at both ends and resonates at frequencies between 1.0 and 2.0 kHz. The problem asks for the speed of traveling waves on the string, which can be solved using the equation f=v/2l and converting kHz to Hz.
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?

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

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

toothpaste666
toothpaste666 said:

## Homework Equations

f = v/2l

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

jz92wjaz said:
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

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.

## 1. What factors affect the speed of a wave on a guitar string?

The speed of a wave on a guitar string is affected by several factors, including the tension of the string, the mass of the string, and the length of the string. The material of the string and the temperature can also have a minor effect on the speed of the wave.

## 2. How does tension affect the speed of a wave on a guitar string?

As the tension on a guitar string increases, the speed of the wave traveling through the string also increases. This is because a higher tension results in a higher frequency of vibration, which in turn increases the speed of the wave.

## 3. Why does the mass of a guitar string affect the speed of a wave?

The mass of a guitar string affects the speed of a wave because it determines the inertia of the string. A higher mass means the string will have a greater resistance to being moved, resulting in a slower speed of the wave. A lighter string will have less inertia and a higher speed of the wave.

## 4. How does changing the length of a guitar string affect the speed of a wave?

The length of a guitar string has a direct effect on the speed of a wave. A shorter string will have a higher speed of the wave, while a longer string will have a slower speed. This is because a shorter string has a shorter distance to travel when vibrating, resulting in a higher frequency and higher speed of the wave.

## 5. Can the speed of a wave on a guitar string be altered by changing the material?

Yes, the material of a guitar string can affect the speed of a wave. Different materials have different densities and stiffness, which can impact the speed of the wave. For example, a steel string will have a higher speed of the wave compared to a nylon string due to its higher density and stiffness.

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