1. PHY 231 1 PHYSICS 231 Lecture 37: standing waves & harmonics Remco Zegers Question hours: Thursday 12:00-13:00 & 17:15-18:15 Helproom

2. PHY 231 2 doppler effect v observer : positive if moving towards to source v source : positive if moving towards the observer source you v source I=P/(4  r 2 )

3. PHY 231 3 applications of the doppler effect: speed radar

4. PHY 231 4 applications of doppler effect: weather radar Both humidity (reflected intensity) and speed of clouds (doppler effect) are measured.

5. PHY 231 5 shock waves what happens if v source  v sound ?

6. PHY 231 6 shock waves II high-pressure wave a lot of energy is stored in the wave (loud bang, vibrations, broken windows) sin  =v sound /v source v source /v sound : Mach Mach 1: speed of sound. Mach 2: 2x speed of sound etc

7. PHY 231 7 shock waves: passing jet

8. PHY 231 8 example you jet A low-flying jet passes by at 300m away from you. When it is 1 km further, you hear the sonic shock-wave. What was the speed of the jet in mach? 300m 1000m

9. PHY 231 9 standing waves Two interfering waves can at times constructively interfere and at times destructively interfere If the two interfering waves always have the same vertical displacement at any point along the waves, but are of opposite sign: standing waves

10. PHY 231 10 How to create standing waves: a rope The oscillations in the rope are reflected from the fixed end (amplitude is reversed) and create a standing wave. demo

11. PHY 231 11 we can produce different wave lengths 1 =2L 2 =L 3 =2L/3 4 =2L/4 5 =2L/5 both ends fixed n =2L/n or L=n n /2

12. PHY 231 12 standing waves both ends fixed n =2L/n or L=n n /2 F: tension in rope  : mass per unit length n th harmonics f 1 : fundamental frequency

13. PHY 231 13 example: the guitar n th harmonics: depends where and how the string is struck note that several harmonics can be present and that non-harmonics are washed out length can be chosen by placing fingers changes from string to string: bass string is very heavy tension can be varied by stretching the wire

14. PHY 231 14 example A guitar string is struck. Assume that the first harmonic is only excited. What happens to the frequency if: a)The player put a finger at half the length of the string? b)The player makes the tension 10% larger (by turning the tuning screw)? c)A string is struck in the same way, but its mass is 3 times higher?

15. PHY 231 15 Standing waves in air columns Just like standing waves in transverse oscillations, one can make standing waves in longitudinal oscillations as well.

16. PHY 231 16 An air column (pipe) A pipe can be open or closed on either or both sides. For now, let’s consider the air-displacements (anti-)nodes

17. PHY 231 17 Both ends open

18. PHY 231 18 One end open, one end closed even harmonics are missing!!!

19. PHY 231 19 example A simple flute is played by blowing air in on one side and the other end is open. The length of the tube can be varied manually (like a trombone). What are the frequencies of the first two possible harmonics if L=0.5m? If the length is made half of the original length, how will these change v=343m/s?

20. PHY 231 20 example A simple flute is played by blowing air in on one side and the other end is closed. The length of the tube can be varied manually (like a trombone). What are the frequencies of the first two possible harmonics if L=0.5m? If the length is made half of the original length, how will these change v=343m/s?