Highest harmonic of a string within typical human's audible range

In summary, the highest harmonic of a string with a length of 16m, linear density of 0.0015 kg/m, and stretched tension of 557N that is within the typical human's audible range (up to 20000 Hz) is 1050 harmonics. This is calculated using the equations v= sqrt ( F/ u), v= lamba * frequency, and lamba = 2 Length / n.
  • #1
hemetite
50
0

Homework Statement



What is the highest harmonic of this string that is within the typical human's audible range (up to 20000 Hz)

String length of 16m
u = liner density = 0.015 g/cm = 0.0015 kg/m
stretched tension of the string = 557N

Homework Equations



v= sqrt ( F/ u)

v= lamba * frequency

lamba = 2 Length / n


The Attempt at a Solution



v= sqrt ( F/ u) = sqrt ( 557/0.0015 ) = 609.37

up to human's typical audible frequency = 20000 Hz

v= lamba * frequency
609.37 = lamba * 20 000 Hz
lamba = 0.0304685

therefore lamba = 2 length /n

0.0304685 = (2* 16) / n

n=1050.265

Ans: the highest harmonic of the string that is within human's audible range = 1050 harmonics.

Am i right?...
 
Physics news on Phys.org
  • #3
thaank...u... :)
 

1. What is the highest harmonic of a string within a typical human's audible range?

The highest harmonic of a string within a typical human's audible range is usually the 7th or 8th harmonic, which corresponds to a frequency that is 7-8 times higher than the fundamental frequency of the string.

2. How is the highest harmonic of a string determined?

The highest harmonic of a string is determined by multiplying the fundamental frequency of the string by the harmonic number. For example, if the fundamental frequency of a string is 100 Hz, the 7th harmonic would be 700 Hz (100 Hz x 7).

3. Can the highest harmonic of a string be higher than the typical human's audible range?

Yes, the highest harmonic of a string can be higher than the typical human's audible range. This will depend on the characteristics of the string, such as its length, tension, and material, as well as the abilities of the individual to perceive high frequencies.

4. Why is the highest harmonic of a string important?

The highest harmonic of a string is important because it contributes to the overall sound and timbre of the string. The presence and strength of higher harmonics can affect the perceived quality of the sound and can be manipulated by musicians to achieve different tones or effects.

5. How does the highest harmonic of a string change with different instruments?

The highest harmonic of a string can vary greatly depending on the type of instrument. For example, a piano string will have a higher highest harmonic compared to a guitar string due to the differences in their construction and materials. Additionally, different playing techniques and styles can also impact the highest harmonic produced by a string.

Similar threads

Harmonic Frequency of a String
    • Introductory Physics Homework Help
Replies
5
Views
1K
How harmonics are produced in a guitar string?
    • Introductory Physics Homework Help
Replies
11
Views
3K
Violin frequencies and harmonics
    • Introductory Physics Homework Help
Replies
2
Views
3K
Linear density and tension problem
    • Introductory Physics Homework Help
Replies
4
Views
4K
What is the relationship between tension and number of loops in a standing wave?
    • Introductory Physics Homework Help
Replies
1
Views
9K
Wavelengths of lowest and highest audible frequencies
    • Introductory Physics Homework Help
Replies
2
Views
2K
Calculating Wave Velocity, Mass, and Wavelength of a Guitar String
    • Introductory Physics Homework Help
Replies
8
Views
7K
Waves on a String: Mass & Standing Wave Mode
    • Introductory Physics Homework Help
Replies
6
Views
20K
How Does Changing String Density Affect Piano Sound Frequency?
    • Advanced Physics Homework Help
Replies
4
Views
1K
Calculating Length, Radius & Frequency of Steel Guitar String
    • Introductory Physics Homework Help
Replies
13
Views
10K

Hot Threads

Recent Insights

Back
Top