Palm Pipe Lab

Music is Math?! How could this be???

First some key vocabulary:

• standing wave: stationary wave that remains in a constant with no net transport of energy
• frequency: shakes per second; measured in Hertz (Hz)
• harmonics: certain frequencies at which standing waves occur
• wavelength: length of wave; measured in meters (m)
• velocity: speed of sound; measured in meters per second (m/s)

Well it turns out that music is a blend of harmonics with whole number ratios in between. The difference between sound and music is that sound produces all different types of frequencies that aren't harmonics and not mathematically proportional; whereas music produces all harmonics at once which we perceive as one because we only hear the peak frequency.


BIG Questions:
1. How can we tell something (like sound) is a wave if it is invisible or too small for us to see?
2. How do musical instruments work?
3. What's the difference between woodwind and a stringed instrument?

Task: figure out what musical note my palm pipe generates.

In order to find the frequency, I measured the length and diameter of my palm pipe and plugged my information into the equation Length = 1/4 (wavelength) - 1/4 (diameter inside)

• length: 14 cm —> .14 m
• diameter: 1.3 cm —> .013 m
• .14 = 1/4 (w) - 1/4 (.013)
• .143 = .25w
• wavelength = .573 m

Then we used the fundamental wave equation to find the frequency:

** speed of sound traveling in air is 343 m/s **

       

    V = f (w)

    343 = f (.573)

    f = 598.604 Hz

We used Wolfram Alpha to figure out what musical note is played by typing in the peak frequency. This musical note plays a D5. We also checked our answer using our Labquest2 that electronically calculated the peak frequency which gave us the same note. THEN we created a palm pipe symphony in the classroom! We played "Twinkle Twinkle Little Star" and it actually sounded like the song!

       

Rainbows and Dispersion

Rainbow

           This is a picture of me spraying a watering hose in the sunlight, which produces a rainbow. How does this beautiful phenomenon occur? Well in physics class this week, I learned the concept of refraction, or the bending of light. Light bends, or changes directions when it travels from one medium to another. This is because light travels at different speeds in different mediums. In this case, light passes through air, then through water, and back into the air. Light refracts into the water, then reflects internally, and refracts once more back into the air. Visible light, which is also known as white light, consists of many colors. Red, orange, yellow, blue, green, and violet separate when passing through a refracted material or specifically a prism. Each droplet of water acts like a prism that disperses the light and reflects it back to your eyes. Because each color has a different frequency, they bend at different angles. Because they bend at different angles, the colors of the rainbow appear in a predictable order each time it rains. This process is called dispersion.

Magnetism

Standard 6.4: How can we use the Right Hand Rule #2 to predict how moving charges are affected by magnetic fields (the direction of the magnetic force on the moving charge)?

Right Hand Rule #1

Right Hand Rule #2

   
  In physics class, we discovered the Right Hand Rule #2 which allows scientists to discover the direction of a magnet's force on a current. Whenever a moving charge comes in contact with another magnet's magnetic field, it experiences a force. "F" is a force on a moving charge as a result of the magnetic field and in this rule, the palm of a hand is represented as the force. In terms of using the Right Hand Rule #2, it would be correct to say that I place my thumb in the left direction because a current is moving left. I curl my fingers away from me going towards the paper on top of the wire, and my fingers curl towards me under the wire. This represents the magnetic field. When I open my fingers, my palm is  facing toward the paper, proving that the magnetic field is going that way. The Right Hand Rule #2 identifies all variables needed to figure out the characteristics of a magnetic field. 

Voltage

The real question is... how is it possible that we can play games, take notes, surf the web, and take videos on our Ipads? How does the Ipad function? Well the Ipad contains a Lithium-ion battery that produces the energy for the Ipad to run on. But how does this battery charge? There's some key information needed in order to understand:

• What is a charge?

• a cell with less elections than protons (positively charged) or a cell with more electrons than protons (negatively charged)

• Who do charges transfer?

• touch: friction
• **like charges repel, opposite charges attract**
• when charges transfer, only electrons move

• Affinity

• cells are either "electron loving" or "electron giving"
• meaning that positively charged cells with less electrons tend to give their electrons away or negatively charged cells with more electrons tend to keep their electrons 
• different materials are naturally positive like human hair, wool, and air
• different materials are also naturally negative like rubber, tape, and polyester

• Voltage

• electric potential that is attractive and repulsive; a field that surrounds charged objects
• voltage is to electricity as height is to gravitational potential energy
• electric potential energy (Ue) is the charge times the voltage.. this is what gives the Ipad juice 
• the higher the voltage, the more charge, the greater the Ue

Real World Connection:

       A Lithium-ion battery is supposed to last 10 hours of use before needing to charge. The battery has a high power density that gives you a long battery life in a light package. When the Ipad is plugged into a charger which is plugged into a wall outlet, electrons are flowing. We use this "mountain" analogy to describe voltage and the charge's path. Objects with a positive charge give their electrons away and "run down the mountain." Objects with a negative charge "run up the mountain" to gain more electrons. The cycle continues when charging the Ipad. The negative charges in the battery run uphill and the positive charges run downhill.

http://www.apple.com/batteries/

Ipad Battery

Projectile Motion Reflection

     In this week's lab, I learned about projectile motion: how it works and how to analyze it. A projectile is an object in which only the force of gravity is acting upon it. Its general path of motion is a parabolic trajectory.

      Using the Video Physics App on our Ipads, we analyzed the path of motion of a basketball when shot in the air. After taking the video, we plotted points along the ball's path through the air. We then used these points to graph the x and y components of the ball's path.

X-Component

      The top graph shows the x position over time. The change in position over the change in time is also known as the slope. The slope is constant in this case. The bottom graph shows the x velocity over time. Because acceleration is the change in velocity over the change in time and we know that the velocity is also constant, there is no acceleration and no net force.

Y-Component

       The top graph shows the y position over time. The change in position over the change in time is the slope and velocity. The graph shows that the slope is not constant; therefore, the object is accelerating. The bottom graph shows the y velocity over time. The decreasing line crosses the x-axis, and at that moment the object has a velocity of 0, which means it is at its peak. The rest of the time it is decreasing.

Forces in 2D and Circular Motion

Big Questions

1. What does it mean to analyze forces in 2D?

          Analyzing forces in 2D means that there are two dimensions that need to be measured, an x-component and a y-component, which make up a force at a certain angle. Once we break the two dimensions up, we can use SOH CAH TOA to find the magnitude of Fx and Fy. Then we can find Fnetx and Fnety to calculate the total force. The photo shows an example:

2. How do forces cause objects to move in a circle?

          Centripetal force is a center-pointing force that causes objects to move in a circle. The force and velocity act perpendicular to each other. The object does accelerate; however, it is not the magnitude that changes, but the direction. The magnitude remains at a constant speed, but the direction keeps changing. Without this centripetal force, an object would continue to move in a straight line, tangent to the circle. In the hover disk lab we did this week, we spun the disk connected to a rope in a circle at a constant speed. When we let go, the disk continued moving, but in a straight line since there was no centripetal force.

3. What does it mean to be an orbit? How do satellites orbit planets? How do planets orbit the sun?

          In the hover disk lab, the disk orbits the person, just as satellites orbit planets and planets orbit the sun. When something is in orbit, it is constantly moving around another object in a circle. When satellites orbit planets, the centripetal force acting on them is gravity, pulling them to the center. A satellite in space is actually moving at a free-fall toward the planet. The satellite moves in a sideways direction and falls into orbit. The planets orbit the sun in the same way.

Newton's Three Laws of Motion

Over the past 2 weeks, we have been deriving Newton's three laws of motion by performing the hover disk lab and the fan cart lab.

Newton's First Law

• An object at rest or traveling at a constant speed will continue to do so, unless a net force acts on it.

• Any object moving at a constant speed or at rest, has no net force acting on it. (Fnet = 0). The hover disk lab allowed us to see how this law works. When the hover disk is at rest or moving at a constant speed, it will not have a change in velocity, or accelerate, because there is no net force acting on it.

• Although there is no net force acting on the object because the object is at rest, there are still many forces acting on everything. In the interaction diagram, you can see that there is a gravitational force acting down on person 1, person 2, the earth, and the hover disk. But what allows them to not fall through the ground is the normal force acting up on them.

• Here is an example where the object remains at a constant speed. Here we see that there is so net force on the object; however, there are still gravitational and normal forces acting on oerson 1, person 2, the disk, and the earth.

Newton's Second Law

• Force = mass (acceleration)

• From the fan cart lab, we derived this equation. We measured the acceleration of a 0.3 kg fan cart when turned on high with a constant force of 0.15 newtons. We then added weights of different masses to the fan cart to find different accelerations. From this we found that acceleration is the change in velocity divided by the change in time.

Collected Data

0.3 kg cart: 0.450 m/sec^2

0.4 kg cart: 0.380 m/sec^2

0.6 kg cart: 0.208 m/sec^2

1.1 kg cart: 0.146 m/sec^2

1.4 kg cart: 0.123 m/sec^2

1.7 kg cart: 0.105 m/sec^2

• To derive this equation, we found that as the mass increases, the acceleration decreases, meaning that mass and acceleration are inversely proportional. We also had to take into account that the force remains constant; therefore, we came up with the equation F = ma.

Newton's Third Law

• When two objects interact, they exert equal and opposite forces on each other.

• These forces are:

• equal in magnitude

• opposite in direction

• same type of force

• The hover disk lab helped us see how this law is true. When the hover disk is moving with a net force and is stopped by person 1's hand, the disc and the hand with exert and equal but opposite force on each other, which will be a normal force. 

Real World Connection

Here is a website that tells how Newton's laws of motion relate to a dancer.

http://physicsofballet.homestead.com/newtonlaws.html