1. If two sounds are only slightly off in terms of frequency The ‘Beats’  Produce a periodic rise and fall of amplitude (volume)  Throbbing Sound = Beats

2. #‘beats’ = how far apart the two frequencies are The ‘Beats’  Ex. Tuning Fork 1: f = 440 Hz Tuning Fork 2: f = *Beat Frequency of 2 Hz?

3. A guitar string produces 4 beats per second when tuned with a 350 Hz tuning fork and 9 beats per second when tuned with a 355 Hz tuning fork. What is the actual frequency of the guitar? Example 8

4. 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

5. When the tension in a particular cord is 75.0 N, the wave velocity is 130.0 m/s. If the length of the cord itself is approximately 26.0 inches (1 in = 25.4 mm), what is the mass of the cord? Example 9

6. 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

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

8. 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

9. 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 )

10. 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.

11. A particular string on a piano is 1.50 m long and has a tension of 400.0 N. It vibrates with a fourth-harmonic frequency of 110.0 Hz. A.What is the mass of this string? B.What are the first three harmonics of this string? Example 10