Length on vibrating section of violin

Click For Summary

Homework Help Overview

The problem involves determining the length of the vibrating section of a violin string, given its wavelength, speed of sound, linear density, and tension. The context is rooted in wave mechanics and the physics of string instruments.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of frequency from the given wavelength and speed of sound. There is an exploration of the relationship between tension, linear density, and length of the string, with some questioning the application of linear density in the calculations.

Discussion Status

Some participants have pointed out potential errors in the original poster's approach, specifically regarding the use of linear density in the velocity expression. There is acknowledgment of a mistake in the calculations, and further clarification is being sought regarding the correct application of the given parameters.

Contextual Notes

Participants note that the linear density was provided, which may have led to confusion in the calculations. There is a recognition of the need for careful handling of units and expressions in the context of the problem.

chicagobears34
Messages
37
Reaction score
0

Homework Statement


A particularly beautiful note reaching your ear from a rare Stradivarius violin has a wavelength of 39.1 cm. The room is slightly warm, so the speed of sound is 344 m/s.

If the string's linear density is 0.560g/m and the tension is 160N , how long is the vibrating section of the violin string?

Homework Equations


f=c/wavelength
f=sqrt(F/(m/L))/(2L)

The Attempt at a Solution


frequency = (344m/s) /(.391m) = 879Hz
879=sqrt(160/(.000560/L))/(2L)
i converted .560g/m to .000560kg/m because force is in Newtons
did algebra and got that length is 10.81m, which is wrong.
Not sure what I did wrong though.
 
Physics news on Phys.org
chicagobears34 said:
879=sqrt(160/(.000560/L))/(2L)
i converted .560g/m to .000560kg/m because force is in Newtons
did algebra and got that length is 10.81m, which is wrong.
Not sure what I did wrong though.
Looks like an arithmetic error. Can't tell what you did wrong if you don't post all your work.
 
You were given the linear density of the string, not its entire mass. So no need to divide it by L in your velocity expression.
 
  • Like
Likes   Reactions: 1 person
yes i was given the linear density, so I shouldn't have done m/L
that's what I what was doing wrong.
Thanks
 
chicagobears34 said:
yes i was given the linear density, so I shouldn't have done m/L
that's what I what was doing wrong.
Thanks
Rats - I noticed that but dismissed it as a typo.
 

Similar threads

Calculating the Planck Length
  • · Replies 3 ·
Replies
3
Views
942
Tension and frequency of a vibrating violin string
  • · Replies 26 ·
Replies
26
Views
8K
What is the length of the vibrating section of the violin string?
  • · Replies 4 ·
Replies
4
Views
12K
Frequencies of the first three overtones in a string?
  • · Replies 2 ·
Replies
2
Views
2K
How Do You Calculate the Wavelength of Sound Waves Emitted by a Violin String?
  • · Replies 4 ·
Replies
4
Views
13K
Violin frequencies and harmonics
  • · Replies 2 ·
Replies
2
Views
4K
Tuning a Violin's Chord (Frequencies)
  • · Replies 9 ·
Replies
9
Views
4K
How to Calculate Wave Velocity in a Tuned Violin String
  • · Replies 2 ·
Replies
2
Views
2K
Waves: fundamental frequency of taut cable
  • · Replies 3 ·
Replies
3
Views
3K
Which Frequency is NOT Possible for a Vibrating String?
  • · Replies 5 ·
Replies
5
Views
2K