1. Harmonics

2. Vibrating Strings…
A string that is fixed at both ends can experience standing waves and therefore harmonic motion.
First harmonic λ=2L
Second harmonic λ= L
Third harmonic λ = 2/3 L
Fourth harmonic λ = ½ L

3. In string instruments…
f= n (v/2L) f is frequency in Hz
n is the harmonic #
v is wave speed(345m/s)
L is length of string

4. In open ended wind instruments…
f= n (v/2L) f is frequency in Hz
n is the harmonic #
v is wave speed(345m/s)
L is length of instrument

5. In closed ended instruments…
f= n (v/4L) f is frequency in Hz
n is the harmonic #
v is wave speed(345m/s)
L is length of instrument
ONLY ODD numbered harmonics will form!!!

6. Example 1:
What are the first 3 harmonics in an open ended instrument which is 2.45m long? Assume that the speed of sound in air is 345m/s.
f= n (v/2L) This is 3 separate problems.
f= 1 (345/2(2.45))= 70.4Hz
f2= 2(345/2(2.45))= 141 Hz
f3= 3(345/2(2.45))= 211 Hz

7. Example 2:
What happens to the fundamental frequency of the instrument in example 1 if one end is closed?
f= n (v/4L)
f= 1(345/ 4(2.45)) = 35.2Hz
Frequency decreased!!!

8. Intrinsic Frequency
Different materials have “intrinsic” frequency which means when stuck or dropped, copper will have a different pitch than steel or iron.
This is like density!

9. Resonance Frequency
One objects natural frequency can set another object into motion…this is known as resonance.
You have probably experienced resonance when a car with a LOUD stereo pulls up next to you at a stop light.
Resonance frequency can cause objects to structural fail.