1. Oscillations 1. Different types of motion:
Uniform motion
1D motion with constant acceleration
Projectile motion
Circular motion
Oscillations
2. Different types of oscillations:
Periodic oscillations
A motion is called periodic when the system comes back to the same physical conditions every time interval T.
Harmonic oscillations (The simplest, the most important type of periodic oscillations)
Chaotic oscillations

2. 3. Harmonic oscillations
Relation between circular motion and simple harmonic oscillations y
r=A x
T – period
f – frequency
ω – angular frequency
A – amplitude
linear equation
Period of SHO is independent from amplitude!
Units:

3. x T
A=xmax t v t a t

4. 4. Hook’s law and simple harmonic motion
Newton’s second law:
Simple harmonic motion:
Question: Two identical masses hang from two identical springs. In case 1, the mass is pulled down 2 cm and released.
In case 2, the mass is pulled down 4 cm and released.
How do the periods of their motions compare?
A. T1 < T2 B. T1 = T2 C. T1 > T2
Period is independent of amplitude!
This is in fact general to all SHM (not only for springs)!

5. Question 1: Mass m attached to a spring with a spring constant k
Question 1: Mass m attached to a spring with a spring constant k. If the mass m increases by a factor of 4, the frequency of oscillation of the mass
A) is doubled
B) is multiplied by a factor of 4
C) is halved
D) is multiplied by a factor of 1/4
Question 2: A 2.0 kg mass attached to a spring with a spring constant of 200 N/m. The angular frequency of oscillation of the mass is __ rad/s.
A) 2 B) 10 C) 60 D) 100

6. 5. The simple pendulum x t mg L If than Example:
Period and frequency are independent from
amplitude!
Add one more slide with examples
Example:

7. Question: A person swings on a swing
Question: A person swings on a swing. When the person sits still, the swing
moves back and forth at its natural frequency. If, instead, the person stands
on the swing, the new natural frequency of the swing is:
A. Greater B. The same C. Smaller
If the person stands, L becomes smaller
Question: Grandpa decides to move to the Moon, and he naturally takes his old pendulum clock with him. But gravity on the Moon is approximately g/6... As a result, his clock is:
A. Too fast B. Too slow
C. Too fast until noon, too slow after noon
The period of the pendulum is longer on the Moon. So each “second according to this clock” is then longer than a real second.
To tune the clock you can move the clock’s disk up.

8. 6. Damped Harmonic Motion
x(t) t
7. Resonance

9. Waves There are many examples of waves: 2. Types of Waves
Seismic waves
Ripples on a pond
Sound
Electromagnetic wave including light
2. Types of Waves
Wave pulses (waves that have short duration – just a quick pulse)
Periodic waves
Special type of periodic waves – sinusoidal waves
Longitudinal wave: the oscillations are along the direction the wave travels.
Transverse wave: the oscillations are transverse (perpendicular) to the direction the wave travels.

10. 3. Sinusoidal waves Wave at fixed x: Wave at fixed t: T Ay T x y λ A t
Sinusoidal waves are periodic
Amplitude: A
Period: T
Wave length:
A periodic wave is periodic in time at fixed position as the wave passes that position. The period of the wave is T. Each particle in the medium oscillates with the same period and in the same way as the wave passes the particle.
A periodic wave is also periodic in space at fixed time. The period of the wave in space is called the wavelength .
Frequency:
Angular
frequency:
Wave
number:

11. 4. Wavelength, period and speed of waves
T - period
The “speed” of a wave is the rate of movement of the disturbance.
It is not the speed of the individual particles!
The speed is determined by the properties of the medium.
Question 1: If you double the wavelength  of a periodic wave and the wave speed does not change, what happens to the wave frequency f ? A) f is unchanged B) f is halved C) f is doubled
Question 2: A sinusoidal wave has a wavelength of 4.00 m and a period of 2.00s. What is the speed of the wave?
Question 3: A sinusoidal wave has a wavelength of 4.00 m and an angular frequency of 3.14 rad/s. What is the speed of the wave?

12. 5. Interference – combination of waves
(an interaction of two or more waves arriving at the same place)
Important: principle of superposition
No shift or shift by
Shift by
Waves source
a) Constructive interference: the interfering waves add up so that they reinforce each other (the total wave is larger)
b) Destructive interference: the interfering waves add up so that they cancel each other (the total wave is smaller or even zero)

13. Example: Two speakers S1 and S2 are driven by the same signal generator and are different distances from a microphone P as shown.
The minimum frequency for constructive interference to occur at point P is __ Hz. (The speed of sound is v = 340 m/s.)
A B C D. 800

14. 6. Diffraction What it is? Haw to observe?
The bending of waves behind obstacles or apertures into the ”shadow region”, that can be considered as interference of many waves.
Haw to observe?
Diffraction is most pronounced when the wavelength of the wave is similar to the size of the obstacle or aperture.
For example, the diffraction of sound waves is commonly observed because the wavelength of sound is similar to the size of doors.
The waves spread out from the opening!

15. Sound
Acoustic waves in the range of frequencies: 20Hz - 20,000Hz
1. Sound waves:
can travel in any solid, liquid or gas
in liquids and gases sound waves are longitudinal ONLY!
longitudinal and transversal sound waves could propagate in solids
Sound in air is a longitudinal wave that contains regions of low and high pressure
Pressure sensor
Vibrating tuning fork
These pressure variations are usually small – a “loud” sound changes the pressure by 2.0x10-5 atm

16. Speed of Sound in Some Common Substances
Substance Speed (m/s)
1. Air (20 oC)
2. Helium (20 oC)
3. Water (0 oC) ,402
4. Lead ,200
5. Human tissue ,540
6. Aluminum ,420
7. Iron and steel ,941

17. 2. Perception of Sound
We use four subjective characteristics to describe how we perceive sound:
pitch, loudness, tone quality and duration
Pitch - how “high” or “low” we perceive sound
(it is directly related to how we perceive frequency)
Combinations of notes that are “pleasing” to the ear have frequencies that are related by a simple whole-number ratio (Pythagoras)
Loudness - how we perceive the amplitude of the sound wave
Loudness manly depends on amplitude and frequency
Tone quality - how we distinguish sounds of the same pitch and loudness (how we perceive the qualities of the waveform)
Duration