Download Sound barrier

SOUND WAVES AND AIR COLUMNS
S.EVANS
SOUND BARRIER & SONIC BOOM
•
•
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
http://www.youtube.com/watch?v=d9A2oq1N38
Sound Barrier
MACH NUMBER
Mach # =
Speed of object
Speed of sound
Example: What is the Mach number for a plane flying
at 1060. km/h in air with a temperature of 6.00
degrees celsius?
DOPPLER EFFECT
“Apparent” change in frequency
DOPPLER EFFECT
http://www.astro.ubc.ca/~scharein/a311/
Sim/doppler/Doppler.html (applet demo)
http://www.youtube.com/watch?v=Tn35S
B1_NYI (Big Bang Theory)
DOPPLER EFFECT
Doppler Effect formula
Doppler Shift
DOPPLER EFFECT
Exercise:
Students…..Prove the Doppler Effect formula from your
knowledge of how the wavelength changes as an object
moves toward you:
2  1  voT
Hint: You will also need to use the universal wave equation.
DOPPLER EFFECT
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?
DOPPLER EFFECT
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.
INTERFERENCE, SUPERPOSITION
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.
INTERFERENCE:
IN PHASE OR OUT OF PHASE?
Wave 1
Wave 2
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?
Wave 3
Wave 4
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?
TRANSMISSION OF WAVES
Waves can speed up or slow down upon entering
a new medium.
Frequency stays the same but wavelength
changes.
REFLECTION OF WAVES
No phase shift upon
reflection
180 degree phase shift
upon reflection
STANDING WAVES
When waves of equal amplitude and
wavelength traveling in opposite directions
interfere a standing wave is formed.
http://www.walterfendt.de/ph14e/stwaverefl.htm
STANDING WAVES
ANTINODES
NODE
What is the internodal distance (distance in
wavelengths between each node)?
STANDING WAVES
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?
MECHANICAL RESONANCE
Requires:
1) An object with a natural frequency
2) 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
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
OPEN AIR COLUMNS
Count have many wavelengths in each of the harmonics:
1st harmonic (fundamental)
2nd harmonic (1st overtone)
3rd harmonic (2nd overtone)
4th harmonic (3rd overtone)
5th harmonic (4th overtone)
CLOSED AIR COLUMNS
Count have many wavelengths in each of the harmonics:
1st harmonic (fundamental)
3rd harmonic (2nd overtone)
5th harmonic (3rd overtone)
AIR COLUMN EXAMPLES
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)
AIR COLUMN EXAMPLES
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)
AIR COLUMN EXAMPLES
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
• 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.
STRINGED INSTRUMENTS
Ex 1: If the fundamental frequency produced by a guitar
string is 400. Hz, what is the frequency of the second
overtone (3rd harmonic)?
STRINGED INSTRUMENTS
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,

STRINGED INSTRUMENTS
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 ?
MUSIC VS NOISE
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)