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

Click For Summary
SUMMARY

The discussion centers on the relationship between tension and wave properties in a nylon guitar string with a linear density of 9.0 g/m and a tension of 180.0 N. The calculated speed of the traveling waves is confirmed to be 141 m/s using the formula v = sqrt(T/u). To determine the wavelength, participants suggest analyzing the standing wave pattern by counting nodes and antinodes, as the frequency is not provided directly.

PREREQUISITES
  • Understanding of wave mechanics, specifically standing waves
  • Familiarity with the wave speed formula v = sqrt(T/u)
  • Knowledge of linear density and its impact on wave properties
  • Ability to identify nodes and antinodes in wave patterns
NEXT STEPS
  • Study the relationship between tension and wave speed in strings
  • Learn how to calculate wavelength using standing wave patterns
  • Explore the concept of nodes and antinodes in oscillating systems
  • Investigate the effects of different materials on wave propagation in strings
USEFUL FOR

Physics students, music educators, and anyone interested in the mechanics of wave behavior in musical instruments.

bearhug
Messages
78
Reaction score
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.
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 23 ·
Replies
23
Views
3K
  • · Replies 29 ·
Replies
29
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 11 ·
Replies
11
Views
5K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 3 ·
Replies
3
Views
7K
  • · Replies 2 ·
Replies
2
Views
2K
Replies
13
Views
2K
  • · Replies 10 ·
Replies
10
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K