Physics 11: 7-16 Waves and interference

Homework

Reading Preparation
Key Equations
WebLecture
Study Activity
Chat Preparation Activities
Chapter Quiz
Lab Work

Reading Preparation

Text Reading: Giancoli, Physics - Principles with Applications, Chapter 11: 7-16

Study Points

11.7: Mechanical wave motion involves the actual physical movement of a material object through space, oscillating away from or toward some origin referent. The frequency and wavelength are related to the speed of the point on the wave by v = f* λ .
11.8: In transverse waves (such as water waves), the amplitude of the wave is at right angles to the direction of motion of the wave. In longitudinal waves, the amplitude of the wave is in the same direction as the direction of motion; it may be easier to visualize longitudinal waves (such as sound waves) as a sequence of compression and rarefaction phases. An isolated oscillation is a pulse; continuous oscillations produce periodic waves. Velocity depends on wavelength and frequency: v = λf (Greek nu ν is sometimes also used for frequency). Amplitude is independent of wavelength and frequency.
11.9: Since waves involve velocity and motion, they carry energy. The amount of energy in a wave is usually expressed in terms of its intensity, I = power/area = energy/time / area. Intensity can be related to amplitude and frequency by substituting in SHM expressions for each.
11.10: How a longitudinal wave is reflected when it reaches a boundary depends on the nature of the boundary. Waves traveled a fixed-end rope are inverted; waves traveling a rope with the end free to slide up and down are not. If a wave reaches a reflecting surface, its angle of reflection (measured from the norm) will equal its angle of incidence.
11.11: Waves which bounce off surfaces move back across subsequent incoming waves. Each wave is an independent event that, like forces, can be added to determine a net amplitude. This is the principle of superposition. Where the net wave is greater than any component, the interference is constructive; where it is less than any component, the interference is destructive.
11.12: Certain kinds of constructive interference create a standing wave: a situation where the moving waves, while changing, add up to a constant result. Standing waves occur on strings fixed at both ends. The endpoints are nodes, and one or more nodes can occur at equal intervals between these points. The interval represents 1/2 of a wavelength, so if the string is L long, we will get standing waves of 1/2L, L, 3/2L, 2L, etc.
[11.13*: Refraction occurs when a wave crosses into a medium with a different density, such that the speed of the wave must change.]
[11.14*:Diffraction occurs when a wave bends around the edge of an obstruction, changing direction without changing velocity.]

Key Equations

Speed of transfers wave on a cord: $v = \sqrt{\frac{F_{T}}{μ}}, F_{T} = tension, μ = mass / unit length$
Speed of longitudinal wave through a solid medium $v = \sqrt{\frac{E}{ρ}}, E = elastic modulus, ρ = density$
Speed of longitudinal wave through a liquid medium $v = \sqrt{\frac{E}{ρ}}, B = bulk modulus, ρ = density$
Intensity of a spherical wave (emanating from point source): $Intensity = \frac{\frac{energy}{time}}{area} = \frac{power}{area} = \frac{P}{4 π r^{2}}$
Energy carried by longitudinal wave:
S = cross-section area
A = amplitude $E = ½ k A^{2} = (2 π^{2} m f^{2}) A^{2} = 2 π^{2} ρ Svt f^{2} A^{2}$
Length of fixed-end string where harmonic n = 1,2,3.... $l = \frac{n λ_{n}}{2}$
Fundamental frequency $f_{1} = \frac{v}{λ_{1}}$
Frequency of harmonic n $f_{n} = \frac{v}{λ_{n}} = n f_{1}$
Law of refraction $\frac{\sin θ_{2}}{\sin θ_{1}} = \frac{v_{2}}{v_{1}}$

Web Lecture

Read the following weblecture before chat: Analyzing Wave Motion

Study Activity

Use the simulation to explore wave motion on a string. Chose oscillate as the first option to explore.

Set damping to zero. Modify the amplitude of the motion. Can you create a standing wave?
Keep damping at zero. Modify the frequency of the motion. Can you create a standing wave?
What happens if you select loose end or no end?
What happens if you add damping?
What happens if you change tension?

Physics simulation Java Applets are the product of the PHET Interactive Simulations project at the University of Colorado, Boulder.

Chat Preparation Activities

Forum question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

Chapter Quiz

Required: Complete the Mastery exercise with a passing score of 85% or better.
Go to the Moodle and take the quiz for this chat session to see how much you already know about astronomy!

Lab Work

If you want lab credit for this course, you must complete at least 18 labs; you may complete more if you are preparing for the AP exam.. One or more lab exercises are posted for each chapter as part of the homework assignment. We will be reviewing lab work at regular intervals, so do not get behind!

Lab Instructions: Standing Waves

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Physics

Chapter 11: 7-16 Assignment