*Edit: Inertia refers to the behavior described in Newton's first law, where a resting object will not move, and a moving object will move at a constant velocity in a constant direction, unless another force acts on it.

-Yes, only the restoring force exists.

-No dissapative forces

-Amplitude remains constant

-0.5kx^2*

-Total energy remains constant

-Energy is not lost

-Displacement/Time is a regular wave

-ma+kx=0 *

-Not a lol of real world examples.

Damped:

-No, because there are dissapative forces.

-There are dissapative forces like friction

-Amplitude decreases over time

-0.5kx^2, but ET decreases over time

-Energy decreases over time

-Energy is converted into heat, sound, etc.

-Displacement/Time shows a wave with amplitude decreasing over time

-ma+kx+bv=0, where b is the damping coefficient *

-Examples include shock absorbers and mass dampers

* Needs reviewing

Musical Instruments and Wave Behavior

What - Musical instruments uses longitudinal waves (Wind and brass instruments) or transverse waves (string instruments) to create standing waves. All instruments are driven damped oscillators, since there is always someone blowing/plucking/bowing on one end, and that the vibrations are converted to sound and emitted.

So What - Musical instruments are very important in our lives because much of the human culture is based on music. In early times when electronics didn't exist, the only way for people to create music is through these systems.

Now What -

1. What does over damping sound like on a string?

2. How does plucking or bowing drive the oscillation?

3. What happens if you drive an oscillation away from its natural frequency?

Question 1 (Paper 1a - Multiple Choice)

A flute can be modeled as a pipe open at both ends. The fundamental frequency produced by the flute is 440 Hz when the air temperature is 20°C. What is the approximate length of the flute?

A. 0.20 m
B. 0.39 m
C. 0.78 m
D. 1.32 m

Question 2 (Paper 2 - Extended Response)

A guitar string is fixed at both ends and vibrates in its second harmonic mode. The string has a length of 0.65 m and produces a note with frequency 392 Hz (G4).

(a) Sketch the standing wave pattern on the string for this mode. [2]

(b) Derive an expression for the frequency of the nth harmonic of a string fixed at both ends in terms of tension T, linear mass density μ, and length L. [4]

(c) Using your expression, calculate the tension in the string if it has a linear mass density of 6.3×10^−4 kg/m. [3]

Travelling waves oscillate at every point, while standing waves have nodes andn antinodes.

Travelling waves travel, while standing waves are trapped between 2 boundaries.

• How does changing the difference in frequency affect the frequency of the wave caused by constructive and destructive interference?

• How do harmonics affect the amplitude, provided the energy remains the same?

• How does pipe width affect the resonance frequency if the length stays constant?

Reflection:

I think the tuning forks were the most interesting, because of their resonating behavior as well as your abillity to tune them using a weight. One thing that surprised me was the constructive destructive interference experiment that I did with the two tuning forks, with one tuned slightly lower than the other. I was not expecting the oscillation to be so obvious. The research question that I am the most interested in is the first one that I wrote.

Constructive interference happens when 2 waves intersect and double up, while destructive interference happens when two opposite waves (peak and trough) meets and cancels each other out.

R0: Radius of a singular nucleon (fermi radius)

V: Volume of nucleus

Rho: Density (constant)

Adiabetic: Really quick, smaller change in V

However, the charge inside the sphere but not in the center behaves differently. In a non-conducting sphere, the field strength increases as you get closer to the surface. In a conductive sphere, the field strength is always 0 inside the sphere.