1 / 14

Sound

Sound. 13.3. Harmonics. A vibrating string will produce standing waves whose frequencies depend upon the length of the string. Harmonics Video 2:34. In the lowest frequency of vibration, one wavelength will equal twice the length of string and its called the fundamental frequency (f 1 ) .

dorjan
Télécharger la présentation

Sound

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sound 13.3

  2. Harmonics • A vibrating string will produce standing waves whose frequencies depend upon the length of the string. Harmonics Video 2:34

  3. In the lowest frequency of vibration, one wavelength will equal twice the length of string and its called the fundamental frequency (f1). For f1, 1λ = 2L One wavelength = 2*length of string Fundamental Frequency Half of a wavelength

  4. Harmonics • A Harmonic series is a series of frequencies that include the fundamental frequency and multiples of that frequency. • 1st harmonic = f1 • 2nd harmonic = f2 = 2*f1 • 3rd harmonic = f3 = 3*f1 • Etc…

  5. Harmonics • The second harmonic is the next possible standing wave for the same string length. • This shows an increase in frequency, and a decrease in wavelength. • f2=2f1 λ2 = L Second Harmonic = 2*fundamental frequency

  6. Harmonics • As the harmonic increases the frequency increases and wavelength decreases. Ex: • f3= 3f1λ3 = 2/3λ1 • f4= 4f1λ4= ½ λ1 • Standing Waves, Fixed at Both Ends Animation

  7. Formula for other harmonics • Harmonic Series of standing waves fn = n* V n=1, 2, 3… 2L Frequency = harmonic number x (speed of waves on the string) (2)*(length of vibrating string)

  8. Standing Waves in an Air Column • If both ends of a pipe are open, all harmonics are present and the ends act as antinodes. • This is the exact opposite of a vibrating string, but the waves act the same so we can still use the same formula to calculate frequencies. fn = n* V n=1, 2, 3… 2L Frequency = harmonic number x (speed of waves on the string) (2)*length of vibrating air column)

  9. Standing Waves in an Air Column • If one end of the pipe is closed, only odd harmonics are present (1, 3, 5, etc). • This changes the formula: fn = n* V n=1, 3, 5… 4L Frequency = harmonic number*(speed of waves on the string) (4)*length of vibrating air column)

  10. Example • What are the first three harmonics in a 2.45 m long pipe that is open at both ends? Given that the speed of sound in air is 345 m/s. • L= 2.45 m v= 345 m/s • fn = n*v/2L • 1st harmonic: f1= 1*(345 m/s)/(2*2.45 m) = 70.4 Hz • 2nd harmonic: f2= 2*(345 m/s)/(2*2.45 m) = 141 Hz • 3rd harmonic: f3= 3*(345 m/s)/(2*2.45 m) = 211 Hz

  11. Example • What are the first three harmonics of this pipe when one end of the pipe is closed? Given that the speed of sound in air is 345 m/s. • L= 2.45 m v= 345 m/s • fn = n*v/4L • 1st harmonic: f1= 1*(345 m/s)/(4*2.45 m) = 35.2 Hz • 3rd harmonic: f3= 3*(345 m/s)/(4*2.45 m) = 106 Hz • 5th harmonic: f5= 5*(345 m/s)/(4*2.45 m) = 176 Hz

  12. Why do different instruments sound different? • Timbre is the quality of a steady musical sound that is the result of a mixture of harmonics present at different intensities. • This is why a clarinet and a trumpet can play the same pitch but they sound different. • Harmonics Applet

  13. Beat • When two waves of slightly different frequencies travel in the same direction they interfere. This causes a listener to hear an alternation between loudness and softness and is called beat.

  14. Beat • Formation of Beats Applet • The frequency difference between two sounds can be found by the number of beats per second.

More Related