1. Traveling Waves Lecture 34 Friday. December 5

2. Exam 4 Average = 88.4

3. Waves Sound Water Electromagnetic Traveling versus Standing

4. Waves on a String Wave on a string-motion perpendicular to string-pulse t=1.34 s t=2.05 s

5. Speed of a wave on a string Linear mass density

6. String Motion is perpendicular to the string and to the direction the wave is moving. Hence a transverse wave.

7. Sound Pressure wave, air particles move back and forth in the direction of propagation—hence a longitudinal wave. Speed in air at t=20 0 C = 343 m/s

8. Graphing a Wave For a fixed x=x 0 we can plot the wave versus time: A “history” graph, motion at a fixed point as a function of time. y(t) t

9. Snapshot Graph For a fixed time, t=t 1 y(x) x

10. Sinusoidal Waves Any wave can be written as the sum of sinusoidal waves—Fourier y depends on x and t – In one period t, wave goes through one oscillation

11. Wave goes through one oscillation if we change x by one wavelength ( a wavelength is the period In space.) Putting these together: For a wave moving to the right, plus x-direction

12. Moving to the left, –x direction

13. How many waves pass a point in one second? How long is this train of waves? Thus

14. Problem 15.13 The motion detector used in physics lab sends out 40 kHz ultrasonic pulses. A pulse goes out, reflects of the object being measured, and returns to the detector. The lab temperature is 20 0 C. A) What is the wavelength? B) time for a round trip to an object 2.5m away?

15. Monday 15: 4-6 Sound and Light Problems 15: 1, 4, 7, 13, 15,,17, 18