Week 3 (Jan 27 - 31)
Read: and Falling Bodies and Pendular Motion (ASGv2 Chap. 4), Pendular motion and harmony (ASGv2 Chap. 5)
Key topics: Periodic motion, pendulums, sound waves, vibrating strings, frequency and pitch, consonance and dissonance, sympathetic resonance
PHY 201 lecture: Drag, nonuniform acceleration, and terminal velocity.
Key topics: Periodic motion, pendulums, sound waves, vibrating strings, frequency and pitch, consonance and dissonance, sympathetic resonance
PHY 201 lecture: Drag, nonuniform acceleration, and terminal velocity.
Homework:
Lab: Harmony (Ex. 5.6). In lab this week, we will be exploring sound using tuning forks, microphones, and logger-pro software. In particular, you should use a microphone to measure and record the pressure as a function of time, P(t), for the following sound sources: (i) a single tuning fork, (ii) two tuning forks separated by one octave, (iii) two tuning forks that are not separated by one octave, (iv) three tuning forks that form a major chord.
For each of your measurements, you will need to find a mathematical function that nicely fits your data. Here are a few pointers for achieving success. (i) don't do the more complicated experiments until you have excellent data for a single tuning fork. be patient. If something doesn't work, change your technique and try again. (ii) use a medium-length tuning fork to start—not too short and not too long. (iii) use the highest sampling rate that logger pro will allow. (iv) For the single tuning fork, change the collection time so that no more than about 5 oscillations occur during the time of data collection. (v). For the chord, you might wish to see 10 or so oscillations to see a pattern.
Strange: Galileo's finger is located in the Museo di Storia del Scienza in Florence, Italy (Hat tip to Rachel Dziekan, who kindly notified me of this link.)
Chapter 4: These 4 videos deal with the effect of drag on falling bodies.
Chapter 5: These four videos deal with Galileo's theory of sound and harmony.
Here are a couple of interesting optional videos: The first is about music (specifically Led Zeppelin); the second is a mesmerizing video depicting pendulum motion.
- Ivory Balls (Ex. 4.1)
- Comparing pendulums (Ex. 4.2)
- Dissonance (Ex. 5.1),
- Suspended weight (Ex. 5.2),
- violin strings (Ex. 5.3). Hint: you will need to look up the frequency of a G and an E note.
- harmony essay (Ex. 5.5)
- PHY 201 problem on drag and terminal velocity: Drag reduces the acceleration of a falling body because it exerts a force opposite the direction of motion of the falling body. As a ball falls through a fluid, the drag force exerted by the liquid increases until the sum of the drag and buoyancy balance the ball's weight. At this time, the ball achieves so-called "terminal velocity." (a) What is the terminal velocity of a 2mm diameter indium ball falling through liquid gallium? Hint: at terminal velocity, the acceleration is zero. Let us assume that the flow around the ball is turbulent (-not- laminar), so that the drag force is given by D = 1/2 * (fluid density) * (cross sectional area of sphere) * (drag coefficient of sphere) * v^2. The drag coefficient of a sphere is approximately 1. (b) Now: repeat this problem for an indium ball if it is submerged in liquid mercury (instead of liquid gallium). In particular: what is its terminal velocity? Does the indium ball ascend or descend?
Lab: Harmony (Ex. 5.6). In lab this week, we will be exploring sound using tuning forks, microphones, and logger-pro software. In particular, you should use a microphone to measure and record the pressure as a function of time, P(t), for the following sound sources: (i) a single tuning fork, (ii) two tuning forks separated by one octave, (iii) two tuning forks that are not separated by one octave, (iv) three tuning forks that form a major chord.
For each of your measurements, you will need to find a mathematical function that nicely fits your data. Here are a few pointers for achieving success. (i) don't do the more complicated experiments until you have excellent data for a single tuning fork. be patient. If something doesn't work, change your technique and try again. (ii) use a medium-length tuning fork to start—not too short and not too long. (iii) use the highest sampling rate that logger pro will allow. (iv) For the single tuning fork, change the collection time so that no more than about 5 oscillations occur during the time of data collection. (v). For the chord, you might wish to see 10 or so oscillations to see a pattern.
Strange: Galileo's finger is located in the Museo di Storia del Scienza in Florence, Italy (Hat tip to Rachel Dziekan, who kindly notified me of this link.)
Chapter 4: These 4 videos deal with the effect of drag on falling bodies.
Chapter 5: These four videos deal with Galileo's theory of sound and harmony.
Here are a couple of interesting optional videos: The first is about music (specifically Led Zeppelin); the second is a mesmerizing video depicting pendulum motion.