Physics 11 Advanced

Mr. Jean

May 16th, 2012

The plan:

• Video clip of the day

• Wave reflection

• Sound Waves in Open Pipe

• Sound waves in Closed Pipe

Doppler Effect:

• http://www.brightstorm.com/science/physics/vibration-and-waves/doppler-effect/

x xx xxxx x xx xxxxx xxxxxx

SubsonicSubsonic

xxxx xxxx xx xxxx xxxx xxxx xx xx

SupersonicSupersonic

Video Demonstration:

Standing Waves:

• http://www.brightstorm.com/science/physics/vibration-and-waves/standing-waves/

Standing Waves in material:

Reflection to fixed ends (Rigid): • For fixed end reflection think of the

medium as being constrained in its motion.

• In the picture to the left you see a string that is securely fixed to the wall.

• The string (the old medium) is free to move up and down, but at the boundary where it meets the new medium (the wall) it is constrained – the string can’t really move up and down like it could before.

• In fixed end reflection, the wave that is reflected back is out of phase by 180.

Reflection for non-fixed (not rigid… “open”):

• In free end reflection, the medium is free to move at the boundary. The reflected wave will be in phase. In the drawing on the right, you see an erect pulse traveling into the boundary being reflected with no phase change. The pulse went in erect and came out erect. Water waves reflecting off a solid wall are a good example of free end reflection.

Sound Waves:

• The disturbance which travels through air is the compression of air molecules – they are squeezed together and pulled apart. Sound is a series of traveling high pressure and low pressure fronts.

Compr ession

Rar ef act ion

W avelengt h

v

Pressure vs. Time

T ime

Pressure

Sound Waves:

• http://www.brightstorm.com/science/physics/vibration-and-waves/sound-waves/

Resonant Air Columns:

• Have you ever blown into a pop bottle and gotten the thing to make a nice, deep, melodious sound? – Bottles can do this because they will

resonate. – When you blow across the top of the bottle,

you create turbulence – bubbles of air – which occur at a broad band of frequencies.

– This is called the edge effect. One of those frequencies is the bottle’s resonant frequency.

Air Columns:

• A standing wave forms in the bottle’s interior. As energy is fed in from the blowing thing, the standing wave gains energy until it is loud enough to hear.

Closed Ended Pipes:

• The reason that the bottle resonates is that a standing wave forms in it. The wavelength of the standing wave has to "fit the bottle", so only the one frequency (or its harmonics) will resonate and be heard. The other frequencies aren't loud enough to be audible. – The closed end of the pipe is a displacement node

because the wall does not allow for the longitudinal displacement of the air molecules.

– As a result, the reflected sound pulse from the closed end is 180 out of phase with the incident wave. The closed end corresponds to a pressure antinode.

Closed End Pipes:

• The open end of the pipe is, for all practical purposes, a displacement antinode and a pressure node. – The reflected wave pulse from an

open end of the pipe is reflected in phase.

– The open end of a pipe is essentially the atmosphere, so no pressure variations take place.

– The reflection actually takes place a slight distance outside the pipe, but we will ignore that.

F irst harmonic

Third harmonic

F ifth harmonic

14

34

54

Harmonics:• Let's look at a simple pipe that

has a standing wave within it. There has to be a displacement node at the closed end and a displacement anti-node at the open end. With this in mind, we can draw in the various standing waves that can form within the pipe. The first one is a quarter of a wave. This is the lowest resonant frequency that can form a standing wave in the tube. Note that the closed end reflects the sound wave out of phase - like a fix-ended wave is reflected.

F irst harmonic

Third harmonic

F ifth harmonic

14

34

54

Closed Ended Pipes:

• Here fn is the harmonic frequency that resonates in the pipe,

• v is the speed of sound, • L is the length of the

pipe, and • n is an integer for the

harmonic that you want.

1, 3, 5, . . .4nv

f n nL

Closed Ended Pipes in general:

• This should go on your formula sheet

• The wavelength for any harmonic would be:

41, 3, 5, . . .n

ln

n

Open Ended Pipes: • Open Ended Pipes:

Open-ended pipes can also resonate. At both ends of the pipe, the wave is reflected in phase. The fundamental wave and associated harmonics would look like this:

• The wavelength is approximately twice the length of the tube. – Note also that the open

ended pipe has all harmonics present.

F irst harmonic

S econd harmonic

Third harmonic

12

22

32

Open Ended Pipes:

• Put this on your formula sheet

1, 2, 3, . . .2nv

f n nL

Musical Instrument Specific Frequencies:

Tuning For k

F lute

C lar inet

Superposition of waves:

1 2 3 4 5 6Har monics

Intensity

1 2 3 4 5 6Har monics

1 2 3 4 5 6Har monics

7 7 8 9

Tuning For k F lute C lar inet

• The last graph (above) shows the intensity of the different harmonics for the same instruments. The tuning fork only has the first harmonic. The flute has a strong 2nd and 4th harmonic. These are stronger than the fundamental frequency. The clarinet has a strong 5th and 1st harmonic. This is why they each sound different to our ears.

Speed of Sound:

• The speed of a sound wave refers to how fast the disturbance is passed from particle to particle; speed refers to the distance in meters which the disturbance travels per unit of time in seconds.

Speed of Sound Lab:

• Complete Speed of sound lab.

• 4 people per group. – All group members are responsible for a

completed lab. – Staple all labs together and marking top lab

only.

• The speed of a sound wave in air depends upon the properties of the air, namely the temperature and the pressure.

v = 331 m/s + (0.6 m/s/C)•T

• where T is the temperature of the air in degrees Celsius. Using this equation to determine the speed of a sound wave in air at a temperature of 20 degrees Celsius yields the following solution.

Calculations for 20 degrees: