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

PHY 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 )

PHY applications of the doppler effect: speed radar

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

PHY shock waves what happens if v source  v sound ?

PHY 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

PHY shock waves: passing jet

PHY 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

PHY 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

PHY 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

PHY 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

PHY 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

PHY 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

PHY 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?

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

PHY 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

PHY Both ends open

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

PHY 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?

PHY 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?