Tension in an oscillating string

In summary, the tension in a 120-cm-long, 3.0 g string oscillating in its n = 4 mode with a frequency of 150 Hz and a maximum amplitude of 5.5 mm is 324. The equation used was f = sqrt(TL/m)/2L, where f is frequency, T is tension, L is string length, and m is mass. However, for more accurate results, the equation v = f*l should be used, where v is velocity and l is wavelength. It is important to not assume the velocity as 343 m/s unless explicitly stated.
  • #1
momopeaches
6
0

Homework Statement


A 120-cm-long, 3.0 g string oscillates in its n = 4 mode with a frequency of 150 Hz and a maximum amplitude of 5.5 mm. Wavelength is 0.6 m.

What is the tension in the string?

Homework Equations


f = sqrt(TL/m)/2L


The Attempt at a Solution



150 = sqrt(1.2T/.003)/2.4

Solving for T gives me
T = 324
Which, according to the program(Mastering Physics), is wrong. I'm not sure if this is the right equation, but its the only found I could find that uses all of the information I have, excluding amplitude.
 
Physics news on Phys.org
  • #2
The 2L only works if the string is at the fundamental harmonic. More generally, the velocity of a wave is v = f*l (in which f is frequency and l is wavelength) and v = Sqr(T/(m/L)), in which T is tension, m is mass, and L is string length.
 
  • #3
Ah, thank you! I got it now. I was assuming 343 m/s for the velocity. Should I not assume, unless the problem explicitly says "through air"?
 

1. What is tension in an oscillating string?

Tension in an oscillating string refers to the force that is pulling the string taut. In other words, it is the amount of stretch or tightness in the string.

2. How does tension affect the oscillation of a string?

The tension in a string is directly proportional to the frequency of oscillation. This means that the higher the tension, the higher the frequency and the faster the string will vibrate. On the other hand, a decrease in tension will result in a lower frequency and slower vibrations.

3. What factors can affect the tension in an oscillating string?

The tension in an oscillating string can be affected by a few different factors. These include the length and thickness of the string, the material it is made of, and the amount of force or weight applied to the string.

4. How does tension impact the pitch of a sound produced by an oscillating string?

The tension in an oscillating string can have a significant impact on the pitch of the sound produced. As mentioned before, higher tension results in higher frequency and therefore a higher pitch. This is why tuning an instrument by adjusting the tension in its strings is essential for producing accurate pitches.

5. Can tension in an oscillating string be changed?

Yes, the tension in an oscillating string can be changed by adjusting the factors that affect it, such as the length, thickness, and weight applied to the string. Additionally, the tension can also be changed by using a tool, such as a tuning key, to tighten or loosen the string.

Similar threads

Finding the frequency of a string based on Mass and Tension
    • Introductory Physics Homework Help
Replies
1
Views
1K
Tension and frequency of a vibrating violin string
    • Introductory Physics Homework Help
Replies
26
Views
6K
Finding the path of an oscillating string
    • Introductory Physics Homework Help
Replies
3
Views
1K
Tension required to tune a string to the note of ##E_2##
    • Introductory Physics Homework Help
Replies
1
Views
1K
What will the wave velocity be in this string?
    • Introductory Physics Homework Help
Replies
15
Views
1K
Foucault Pendulum at the North Pole
    • Introductory Physics Homework Help
Replies
9
Views
682
Harmonic Frequency of a String
    • Introductory Physics Homework Help
Replies
5
Views
1K
Tension in the string of a simple pendulum
    • Introductory Physics Homework Help
Replies
4
Views
3K
Frequency of a wave at resonance
    • Introductory Physics Homework Help
Replies
14
Views
1K
Finding the damping force for a critically damped oscillator
    • Introductory Physics Homework Help
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top