1. What about the rubber bands determines pitch? Musical Instruments - Strings  The pitch or frequency of a string is determined by the string’s velocity (how fast it can move back and forth) F T = Force of Tension m/L = (mass)/(Length) = Linear Density  Tension  Thickness

2. A metal guitar string has a linear mass density of (m/L) = 3.2 x 10 -3 kg/m. What is the velocity of a wave produced by this string when its tension is 90.0 N? Example 8

3. When the tension in a particular cord is 75 N, the wave velocity is 130 m/s. If the length of the cord itself is approximately 26 inches (1 in = 25.4 mm), what is the mass of the cord? Example 9

4. Standing Wave – aka Stationary Waves – waves that appear still. Created by overlapping waves. Standing Waves  Two Parts of a Standing Wave  Nodes: No movement  Anti-Nodes: Maximum vibration

5. Sound (musical notes) will have some sort of repeating pattern Difference Between Notes and Noise

6. Tuning Forks – Produce one frequency (pure tone) Standing Waves w/ Musical Instruments  When a note is played, the primary sound = Fundamental frequency  Within each fundamental frequency are other frequencies – The harmonics  Musical instruments sound different from tuning forks – due to their timbre (tone quality or tone color)  Difference in timbre – due to the instruments harmonics

7. Standing Waves - Strings  Different frequencies are produced by different harmonics  Fundamental  First Harmonic (f 1 )  Number of Loops = 1  Second Harmonic (f 2 )  Number of Loops = 2  f 2 =2(f 1 )  Third Harmonic (f 3 )  Number of Loops = 3  f 3 =3(f 1 )  Fourth Harmonic (f 4 )  Number of Loops = 4  f 4 =4(f 1 )

8. Frequencies for standing waves: Standing Waves - Strings n = number of the harmonic L = Length of the vibrating string v = velocity of a string *Different notes are achieved by changing the length of the vibrating string.

9. A violin string is under a force of tension of 87.0 N. The vibrating portion of the string is 32.0 cm long and has a mass of 0.35 g. The string begins vibrating, creating a fundamental frequency. A.What is the velocity if this string under such conditions? B.What is the fundamental frequency produced? C.What are the values of the second and third harmonics for this fundamental? Example 10

10. A string of length 0.26 m is fixed at both ends. The string is plucked and a standing wave is set up that is noticeably vibrating at its second harmonic. The traveling waves that make up the standing wave have a speed of 155 m/s. What is the frequency of vibration? Example 11

11. These instruments create standing waves using vibrating columns of air Standing Waves – Woodwinds and Brass  Two Categories:  Instruments (Pipes) Open at Both Ends  Instruments (Pipes) Open at One End  Most reed and double-reed instruments: Clarinet, Oboe, Saxophone, Bassoon, etc..  All brass instruments, flute, organ