Wave speed and distance on a guitar string

In summary, the question discusses the wave speed in a guitar string and how pulses move in both directions and are reflected off the ends of the string. It asks for the distance from the other end of the string where two pulses would meet if the string was plucked 25.1 cm from the left end. The solution involves setting up an equation and measuring the distance from the right hand side.
  • #1
jl39845
2
0

Homework Statement


The wave speed in a guitar string of length 62.9 cm is 278 m/s. you pluck the center of the string by pulling it up and letting go. Pulses move in both directions and are reflected off the ends of the string. If you plucked the string 25.1 cm from the left end of the string, how far from the other end of the string would the two pulses meet? In units of cm.


Homework Equations


I thought just some old-fashioned algebra could do it..


The Attempt at a Solution


What I first tried was 25.1 cm + x= Remainingcm-x, so:

25.1cm+x=(62.9-25.1)-x
25.1cm+x=37.8-x
2x=12.7
x=6.35 cm

However, this did not work.

Can anyone tell me what I'm doing wrong? Thanks.
 
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  • #2
Waves meet at P a distance x from B
stringwave.png


Just be careful setting up the equation.
Measure x from the right hand side as the question asks and you can't go wrong.
 

FAQ: Wave speed and distance on a guitar string

1. What is wave speed on a guitar string?

Wave speed on a guitar string is the rate at which the wave travels along the string. It is typically measured in meters per second.

2. How is wave speed related to the tension and mass of the string?

Wave speed on a guitar string is directly proportional to the tension and inversely proportional to the mass of the string. This means that as tension increases, wave speed also increases, and as mass increases, wave speed decreases.

3. Does wave speed change as the string is plucked at different points?

Yes, the wave speed on a guitar string can change depending on where it is plucked. The closer the plucked point is to the end of the string, the slower the wave speed will be. This is because the tension decreases as you move away from the fixed end, causing the wave speed to decrease.

4. How does the distance between frets affect wave speed on a guitar string?

The distance between frets does not directly affect wave speed on a guitar string. However, it can indirectly affect wave speed by changing the length of the vibrating portion of the string. A shorter vibrating length will result in a higher wave speed, while a longer vibrating length will result in a lower wave speed.

5. Is there a maximum wave speed that can be achieved on a guitar string?

Yes, there is a maximum wave speed that can be achieved on a guitar string. This is known as the speed of sound in the material of the string, and it is dependent on the material's density and stiffness. For most guitar strings, the maximum wave speed is around 200 meters per second.

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