1. Oscillations and Waves

2. Pendulum
Harmonic wave with only one frequency N W

3. Mass on a spring
Harmonic wave with only one frequency

4. Displacement vs time Displaced systems oscillate
around stable equil. points
amplitude
Equil. point
period (=T)

5. Simple harmonic motion
Pure Sine-like curve T
Equil. point
T= period = time for 1 complete oscillation
= 1/T
f = frequency = # of oscillations/time

6. Masses on springs
Animations courtesy of Dr. Dan Russell, Kettering University

7. Not all oscillations are nice Sine curves
Equil. point T
f=1/T

8. Natural frequency
f= (1/2p)k/m
f= (1/2p)g/l

9. Driven oscillators
natural freq. = f0
f = 0.4f0
f = 1.1f0
f = 1.6f0

10. Mechanical Resonance
Mechanical resonance is the tendency of a mechanicalsystem to respond at greater amplitude when the frequency of its oscillations matches the system's natural frequency of vibration (its resonance frequency or resonant frequency) than it does at other frequencies.
The system responded as the frequency of its oscillations matched the natural frequency of vibration due to the wind.

11. Resonance in a wave
Resonance - The increase in amplitude of oscillation of an electric or mechanical system exposed to a periodic force whose frequency is equal or very close to the natural undamped frequency of the system.

12. Waves
Animations courtesy of Dr. Dan Russell, Kettering University

13. Wave in a string
Animations courtesy of Dr. Dan Russell, Kettering University

14. Pulsed Sound Wave

15. Harmonic sound wave

16. Harmonic sound wave

17. V=fl or f=V/ l Harmonic wave =v =l l T = = fl = but 1/T=f distance
Wave speed =v
Shake end of
string up & down
with SHM period = T
wavelength =l l T
distance
time
wavelength
period
Wave speed = v = =
= fl =
V=fl or f=V/ l
but 1/T=f

18. Reflection (from a fixed end)
Animations courtesy of Dr. Dan Russell, Kettering University

19. Reflection (from a loose end)
Animations courtesy of Dr. Dan Russell, Kettering University

20. Adding waves pulsed waves
Animations courtesy of Dr. Dan Russell, Kettering University

21. Two waves in same direction with slightly different frequencies
Adding waves
Two waves in same direction with
slightly different frequencies
Wave 1
Wave 2
resultant wave
“Beats”
Animations courtesy of Dr. Dan Russell, Kettering University

22. Adding waves harmonic waves in opposite directions incident wave
reflected wave
resultant wave
(standing wave)
Animations courtesy of Dr. Dan Russell, Kettering University

23. Confined waves Only waves with wavelengths that just fit in survive
(all others cancel themselves out)

24. Harmonics
For every given frequency, there are other frequencies that perfectly fit in the same space. These are called harmonics. They are whole divisions of the original wavelength, or multiples of the basic frequency. This is well known in musical instruments.

25. Allowed frequencies l= 2L f0=V/l = V/2L f1=V/l = V/L=2f0 l=L l=(2/3)L
Fundamental tone
f1=V/l = V/L=2f0
l=L
1st overtone
l=(2/3)L
f2=V/l=V/(2/3)L=3f0
2nd overtone
l=L/2
f3=V/l=V/(1/2)L=4f0
3rd overtone
l=(2/5)L
f4=V/l=V/(2/5)L=5f0
4th overtone

26. Ukuleles, etc l0 = L/2; f0 = V/2L l1= L; f1 = V/L =2f0
l2= 2L/3; f2 = 3f0 L
l3= L/2; f3 = 4f0
Etc…
(V depends on the
Tension & thickness
Of the string)

27. Standing waves in a closed tube

28. Standing waves in an open pipe

29. Doppler effect

30. Sound wave stationary source
Wavelength same in all directions

31. Sound wave moving source
Wavelength in forward direction is shorter (frequency is higher)
Wavelength in backward direction is longer (frequency is higher)

32. Waves from a stationary source
Wavelength same in all directions

33. Waves from a moving source
Wavelength in backward direction is longer (frequency is higher)
Wavelength in forward direction is shorter (frequency is higher)