How Does Tension Affect the Speed and Wavelength of Waves in a Guitar String?

In summary, the conversation discusses the calculation of the speed and wavelength of the traveling waves causing a standing wave on a nylon guitar string. The speed is calculated to be 141 m/s using the equation v=sqrt(T/u). The wavelength is determined by counting the nodes/antinodes in the standing wave pattern.
  • #1
bearhug
79
0
A nylon guitar string has a linear density of 9.0 g/m and is under a tension of 180.0 N. The fixed supports are L = 80.0 cm apart. The string is oscillating in the standing wave pattern shown in the figure. Calculate the speed of the traveling waves whose superposition gives this standing wave. (m/s)

The speed I calculated to be v=sqrt(T/u) = 141 m/s and I know this is right

Calculate the wavelength of the traveling waves whose superposition gives this standing wave. (m)

There are several equations I have been looking at to try and figure out the wavelength. v=lambda(f) but I don't have f.
k=2pi/lambda but I don't have k. I thought that maybe 0.8m would be considered x and use a sinusoidal equation but I still am lacking the amplitude and w. I just need some guidance on this problem.
 
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  • #2
bearhug said:
The string is oscillating in the standing wave pattern shown in the figure.
You can figure out the wavelength by studying the pattern. Hint: Count the nodes/antinodes.
 
  • #3


As a scientist, your calculations for the speed of the traveling waves appear to be correct. To calculate the wavelength, you can use the equation v = λf, where v is the speed of the wave, λ is the wavelength, and f is the frequency. In this case, the frequency can be calculated using the equation f = nv/2L, where n is the number of nodes in the standing wave pattern (in this case, n = 1). Plugging in the values, we get:

v = λf
141 m/s = λ(1/2)(141 m/s)/(0.8 m)
λ = 0.8 m

Therefore, the wavelength of the traveling waves is 0.8 meters. This is equal to twice the distance between the fixed supports (L = 80.0 cm = 0.8 m), which is expected for a standing wave pattern.
 

Related to How Does Tension Affect the Speed and Wavelength of Waves in a Guitar String?

1. What is a guitar string standing wave?

A guitar string standing wave is a type of sound wave that is created when a guitar string is plucked or strummed. The vibration of the string creates a pattern of peaks and valleys that appear to be standing still, hence the name "standing wave."

2. How is a guitar string standing wave formed?

A guitar string standing wave is formed when a guitar string is plucked and the sound waves created travel back and forth along the string. When these waves reflect off of both ends of the string, they interfere with each other and create a standing wave pattern.

3. What factors influence the frequency of a guitar string standing wave?

The frequency of a guitar string standing wave is influenced by several factors, including the tension of the string, the length of the string, and the density of the string. Higher tension, shorter length, and lower density will result in a higher frequency standing wave.

4. How does a guitar player control the frequency of a standing wave on a string?

A guitar player can control the frequency of a standing wave on a string by changing the length of the string, either by pressing down on the frets or by using a capo. They can also change the tension of the string by adjusting the tuning pegs.

5. What is the significance of guitar string standing waves in music?

Guitar string standing waves are significant in music because they determine the pitch of the notes produced by the guitar. By controlling the frequency of the standing wave, a guitar player can produce different notes and create melodies and harmonies. Understanding standing waves is also important for guitar setup and maintenance.

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