# Solve Homework: Sound Waves Lengths in Tube w/ 85cm Guitar String

• Arbitrary
In summary, by plucking a 85cm long guitar string with a fundamental frequency of 350Hz and increasing its tension to achieve a wave speed of 1000m/s, a closed tube next to the string will produce a loud sound. To find the possible lengths of the tube, we can use the equation speed = wavelength*frequency and solve for wavelength, which is equal to 1.7 meters. However, since the speed of the wave inside the tube may not be the same as on the guitar string, further calculations are needed to determine the exact frequency of the sound produced by the tube.
Arbitrary

## Homework Statement

A guitar string that is 85cm long is plucked. The fundamental frequency of the string is 350Hz. The string's tension is then increased and its wave speed is 1000m/s The string is vibrating at its fundamental frequency and a closed tube is next to it. A loud sound is produced by the tube. What are the possible lengths of the tube?

## Homework Equations

speed = wavelength*frequency

## The Attempt at a Solution

1000 = wavelength*frequency
wavelength = 0.85(2) = 1.7
1000 = 1.7*f
f = 588.2

I'm not sure what to do next. I know the speed of the wave inside the tube isn't going to be the same as its speed on the guitar string since they're different mediums, but I'm not sure what that speed would be.

If the sound isoud, what does that tell you about the frequency of the sound wave in relation to the fundamental frequency of the tube?

Additionally, I'm not sure how the tube's length would affect the frequency of the sound produced. Can you provide more information on the setup and any other relevant equations or concepts that may be helpful in solving this problem?

Also, the length of the tube will affect the wavelength, so there may be multiple possible lengths for the tube that would produce a sound at 588.2Hz. To determine the possible lengths of the tube, we would need to use the equation v = f*lambda, where v is the speed of sound in the tube (which can be calculated using the speed of sound in air and the properties of the tube, such as its diameter and material), f is the frequency of the sound produced by the vibrating string, and lambda is the wavelength of the sound wave in the tube. By plugging in different values for lambda, we can determine the corresponding lengths of the tube that would produce a sound at 588.2Hz. Additionally, we would need to take into account any harmonics or overtones of the fundamental frequency that may also produce a sound at 588.2Hz. Overall, there are multiple factors to consider in order to accurately determine the possible lengths of the tube that would produce the desired sound frequency.

## 1. How do sound waves affect the length of a tube?

Sound waves travel through a tube at a specific speed, determined by the properties of the medium (such as air or water). The length of the tube affects the wavelength of the sound waves, as longer tubes allow for longer wavelengths and shorter tubes allow for shorter wavelengths.

## 2. How is the length of a guitar string related to the sound it produces?

The length of a guitar string determines the frequency of the sound it produces. A shorter string will vibrate at a higher frequency, producing a higher-pitched sound, while a longer string will vibrate at a lower frequency, producing a lower-pitched sound.

## 3. How does the length of a guitar string affect the sound waves in a tube?

The length of a guitar string affects the wavelength of the sound waves it produces, which in turn affects the resonance of the tube. This means that the length of the tube will need to be adjusted to match the wavelength of the string in order to produce a clear and resonant sound.

## 4. What is the formula for calculating the wavelength of sound waves in a tube?

The formula for calculating the wavelength of sound waves in a tube is:
Wavelength = 4L/n
Where L is the length of the tube and n is the number of nodes (points where the sound waves cancel out) present in the tube.

## 5. How can understanding sound wave lengths in a tube help improve guitar playing?

Understanding sound wave lengths in a tube can help guitar players adjust the length of the tube (or the length of the guitar string) to produce a clear and resonant sound. This can improve the overall sound quality of their playing and help them achieve a desired tone or pitch.

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