• Sound barrier is the buildup of sound waves in front of an object moving near the speed of sound.

• Sonic boom is created when an object breaks the sound barrier

Sound Barrier

http://www.youtube.com/watch?v=-d9A2oq1N38

Mach # = soundofSpeed

objectofSpeed

Example: What is the Mach number for a plane flying at 1060. km/h in air with a temperature of 6.00 degrees celsius?

“Apparent” change in frequency

http://www.astro.ubc.ca/~scharein/a311/Sim/doppler/Doppler.html (applet demo)

http://www.youtube.com/watch?v=Tn35SB1_NYI (Big Bang Theory)

Doppler Shift

Doppler Effect formula

Exercise:

Students…..Prove the Doppler Effect formula from your knowledge of how the wavelength changes as an object moves toward you:

Hint: You will also need to use the universal wave equation.

Tvo 12

Example: A car travelling at 100. km/h sounds its horn as it approaches someone. If the horn's frequency is 440. Hz and the air temperature is 0.00 degrees celsius, what frequency will be heard as the car  a) Approaches? b) Passes by?       

Example:

In figures (a), (b), (c), (d) and (e) S is a source of sound of real frequency n and L is a listener. The speeds of the source and the listener are equal in all cases except in (e) where the source is at rest and the listener is moving. There is no wind. Pick out the wrong statement from the following:(a) In the case shown in figure (a) the apparent frequency as heard by the listener is equal to the real frequency of the source.(b) In the case shown in fig (b) the apparent frequency as heard by the listener is the greatest.(c) In the case shown in fig (c) the apparent frequency as heard by the listener is the least.(d) In the case shown in fig (d) the apparent frequency as heard by the listener is less than the real frequency of the source.(e) In the case shown in fig (e) the apparent frequency as heard by the listener is greater than the real frequency of the source.

www.acs.psu.edu/drussell/Demos/superposition/superposition.html

Interference:When two waves interact, they are said to interfere with each other.

Principle of Superposition: When two or more waves combine to produce a single wave. The resulting amplitude is the sum of the amplitudes of the individual waves.

Wave 1

Wave 2

Wave 3

Wave 4

1. How many wavelengths are in each of the waves?

2. Are waves 1 and 2 “in” or “out” of phase?3. What do you think would happen if they were

combined (superposition)?4. If two waves with the same frequency are offset

by zero time, they will be in phase. What other offsets (measured in wavelengths) will result in the waves being in phase?

5. Are waves 3 and 4 “in” or “out” of phase?6. What do you think would happen if they were

combined (superposition)?7. What offsets are required for these waves to be

out of phase?

Waves can speed up or slow down upon entering a new medium. Frequency stays the same but wavelength changes.

180 degree phase shift upon reflection

No phase shift upon reflection

http://www.walter-fendt.de/ph14e/stwaverefl.htm

When waves of equal amplitude and wavelength traveling in opposite directions interfere a standing wave is formed.

NODE

ANTINODES

What is the internodal distance (distance in wavelengths between each node)?

Ex.A standing wave has a distance of 80 cm between five consecutive nodes.a)What is the wavelength of the wave? b)What is the speed of the wave if the source frequency is 20 Hz?

Requires:1)An object with a natural frequency2)A forcing function at the same frequency as the natural frequency of the object.3)A lack of energy loss (damping).

Ex. A swing. The swing has a natural frequency and you are the forcing function pushing at the same timing. The swing will keep going higher and higher.

Tacoma Narrows Bridge You tube http://www.youtube.com/watch?v=P0Fi1VcbpAI

Acoustical resonance produces the sounds in musical instruments. ANTINODES

NODE

Open Air columns (at both ends)Ex. Flute, organ pipes, oboe

Closed Air columns (closed at one end)Ex. clarinet

1st harmonic (fundamental)

2nd harmonic (1st overtone)

3rd harmonic (2nd overtone)

4th harmonic (3rd overtone)

5th harmonic (4th overtone)

Count have many wavelengths in each of the harmonics:

Count have many wavelengths in each of the harmonics:

1st harmonic (fundamental)

3rd harmonic (2nd overtone)

5th harmonic (3rd overtone)

Ex 1: The first resonant length of a closed air column occurs when the length is 18.0 cm. What is the wavelength of the sound? If the frequency is 512 Hz, what is the speed of sound?

(Ans. 72.0 cm, 369 m/s)

Ex 2: If the frequency in a closed air column is 256 Hz and the speed of sound is 344 m/s, what is the second resonant length?

(Ans. 1.01 m)

Ex 3: An organ pipe 3.60 m long, open at both ends, produces a musical note at its fundamental frequency. What is the wavelength of the note produced? What is the frequency?

(Ans. 7.20 m, 47.8 Hz)

• Stringed instruments are closed at both ends (violin, guitar. piano).

• Knowing this draw the 1st, 2nd, 3rd and 4th harmonic standing wave patterns for a stringed instrument.

Ex 1: If the fundamental frequency produced by a guitar string is 400. Hz, what is the frequency of the second overtone (3rd harmonic)?

Four factors affect the frequency, f, of vibration of a string:

1)Length,L      1)Tension, T     1)diameter of the string, d      1)density of the string,

Ex 2: A vibrating string has a frequency of 256 Hz. What will the frequency be if:a)The tension in the string is doubled?b)The tension in the string is doubled, the length is doubled and the diameter of the string is reduced by a factor of 3 ?

Use these applets to distinguish the difference between noise and music. http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=17(input harmonics and show how the sound is pleasing and waveform symmetrical)

http://www.wolframalpha.com/widget/widgetPopup.jsp?p=v&id=12ec56cbbe31763b62daf815a2e478b6&title=Timbre&theme=red&i0=256&i1=512&i2=768&i3=1024&podSelect=&showWarnings=1(input random frequencies and show how the sound is noise and waveform random)