PHY138 – Waves, Lecture 3

1. PHY138 – Waves, Lecture 3 “..imagine a stadium full of people doing "the wave" with a giant sheet covering them so that none of the spectators can be seen. To someone watching such an event it would appear that something was moving around the stadium under this sheet. It would look as if some giant creature was running in circles. In reality no one moves around the stadium; each spectator simply stands up and sits back down in the same seat. There is energy moving around the stadium while the people remain stationary.” - thinkquest.org

2. Reading Assignment • Please read the following from Serway and Jewett before class on Wednesday: Chapter 13, Sections 13.7 and 13.8, and Chapter 14, Sections 14.1 and 14.2 • A Web-CT quiz is due Wednesday morning, which tests your basic familiarity with Chapter 14 assigned reading. • McDermott Tutorials book, page 149 regarding Electromagnetic Waves

3. Written Homework Please complete Problems 8, 22, 34 and 41 from Chapter 13. They are due in your tutorial drop-box by Monday, November 22 at 5:00 PM.

4. Note from David Harrison: • Regarding Test 1: Problem involving two horse teams pulling a set of connected hemispheres: • Both the correct answer and “Answer C” were marked as correct. Students who interpreted the question to be about net-force were correct to reason that the net-force on a non-accelerating object is always zero. • Harrison will not answer emails about this question

5. Last day’s lecture: some comments • The simple pendulum was modeled as a point-mass on a massless string. Moment of inertia was therefore I=mr2=mL2. • Objects such as bridges, trumpets, radio antennae, etc, all have natural oscillation frequencies. Resonance occurs when an outside driving force is close to one of these frequencies. At resonance, the amplitude of oscillations is very high.

6. First mini-quiz A person swings on a swing. When the person sits still, the swing oscillates back and forth at its natural frequency. If, instead, two people sit on the swing, the natural frequency of the swing is 1. greater 2. the same 3. smaller

7. Second mini-quiz A person swings on a swing. When the person sits still, the swing oscillates back and forth at its natural frequency. If, instead, the person stands on the swing, the natural frequency of the swing is 1. greater 2. the same 3. smaller

8. PHY138 – Waves, Lecture 3Today’s overview • Mathematical Description of a Wave • Speed of Waves on a String • Reflection and Transmission of Waves • Sound, Ultrasound

9. Sinusoidal Wave snapshot k=2π/λ

10. Sinusoidal Wave at a point in space ω=2π/T

11. Reflection of Transverse Wave Pulse • A pulse traveling to the right on a heavy string attached to a lighter string • Speed suddenly increases

12. Reflection of Transverse Wave Pulse • A pulse traveling to the right on a light string attached to a heavier string • Speed suddenly decreases

13. Reflection of Transverse Wave Pulse • Reflection of a traveling pulse at the free end of a stretched string.

14. Reflection of Transverse Wave Pulse • Reflection of a traveling pulse at the fixed end of a stretched string.

15. Physics of Ultrasound • Speed of sound in bone, flesh and blood are all different • When the speed of any wave suddenly changes, there is a reflection and transmission • Ultrasound images are formed from reflected high frequency sound • Image resolution is set by wavelength, λ • λ=v/f, so higher frequency yields smaller λ, and better resolution

16. Speed of sound in humans