S o u n d

S p e e d o f S o u n d The relationship of the speed of sound vw, its frequency f, and its wavelength y is given by v w = fy In air, the speed of sound is related to air temperature T by v w = (331 m/s) + (0.6 T C ) Where T C represents the temperature of the air in o C

S o u n d I n t e n s i t y a n d S o u n d L e v e l

I n t e n s i t y Intensity is the same for a sound wave as for all waves; it’s given as: I = P / A Where P is the power crossing area A. The SI unit for I was watts per meter squared. The intensity of a sound wave is also related to the pressure amplitude Sound Intensity level in units of decibels (dB) is ß (dB) = 10 log 10 (I/I 0 )

L o u d n e s s Threshold of Hearing (TOH)1* W/m 2 0 dB10 0 Rustling Leaves1* W/m 2 10 dB10 1 Whisper1* W/m 2 20 dB10 2 Normal Conversation1*10 -6 W/m 2 60 dB10 6 Busy Street Traffic1*10 -5 W/m 2 70 dB10 7 Vacuum Cleaner1*10 -4 W/m 2 80 dB10 8 Large Orchestra6.3*10 -3 W/m 2 98 dB Walkman at Maximum Level1*10 -2 W/m dB10 Front Rows of Rock Concert1*10 -1 W/m dB10 11 Threshold of Pain1*10 1 W/m dB10 13 Military Jet Takeoff1*10 2 W/m dB10 14 Instant Perforation of Eardrum1*10 4 W/m dB10 16

H e a r i n g

I n v e r s e S q u a r e L a w The surface area of a sphere is A = 4πr 2 Notice that since the surface area is a function of the square of the radius, then the intensity of sound decreases exponentially.

D o p p l e r E f f e c t a n d S o n i c B o o m s

D o p p l e r

A fire truck is moving at a fairly high speed, with its siren emitting sound at a specific pitch. As the fire truck recedes from you which of the following characteristics of the sound wave from the siren will have a smaller measured value for you than for a fireman in the truck? Choose two characteristics. (A) frequency (B) wavelength (C) speed (D) intensity

D o p p l e r

S o n i c B o o m

D o p p l e r E f f e c t

S t a n d i n g W a v e s I n A i r C o l u m n s

A i r C o l u m n

S t a n d i n g W a v e s A graph of air displacement along the length of the tube shows none at the closed end, where the motion is constrained, and a maximum at the open end. This standing wave has one-fourth of its wavelength in the tube, so that λ = 4L.

S t a n d i n g W a v e s

Another resonance for a tube closed at one end. This has maximum air displacements at the open end, and none at the closed end. The wavelength is shorter, with three-fourths λ′ equaling the length of the tube, so that λ′ = 4L / 3. This higher-frequency vibration is the first overtone.

S t a n d i n g W a v e s The fundamental and three lowest overtones for a tube closed at one end. All have maximum air displacements at the open end and none at the closed end.

S t a n d i n g W a v e s

H o r n B e l l One role for the flared bell on the end of a trumpet is to allow the air to expand outward gradually. This decreases the overshoot of the oscillating air. Less energy reflects from the open end, so that more energy leaves the horn. The horn is louder.

A c o u s t i c I m p e d e n c e

Common NameFrequency Multiple of Fundamental Ratio within octave Fundamental110Hz A21x1/1 = 1x Octave220Hz A32x2/1 = 2x Perfect Fifth330Hz E43x3/2 = 1.5x Octave440Hz A44x4/2 = 2x Major Third550Hz C#55x5/4 = 1.25x Perfect Fifth660Hz E56x6/4 = 1.5x Harmonic seventh770Hz G57x7/4 = 1.75x Octave880Hz A58x8/4 = 2x

M u s i c What gets put into a musical instrument is vibrations or waves covering a spread of frequencies (for brass, it's the buzzing of the lips; for reeds, it's the raucous squawk of the reed; for percussion, it's the relatively indiscriminate pounding; for strings, it's plucking or scraping; for flutes and organ pipes, it's blowing induced turbulence). What gets amplified is the fundamental frequency plus its multiples. These frequencies are louder than the rest and are heard. All the other frequencies keep their original amplitudes while some are even de-amplified. These other frequencies are quieter in comparison and are not heard. Waves interacting in two dimensions causes sand to build up along nodes. This occurs where interacting waves create destructive interference

You don't need a musical instrument to illustrate this principle. Cup your hands together loosely and hold them next to your ear forming a little chamber. You will notice that one frequency gets amplified out of the background noise in the space around you. Vary the size and shape of this chamber. The amplified pitch changes in response. This is what people hear when the hold a seashell up to their ears. It's not "the ocean" but a few select frequencies amplified out of the noise that always surrounds us. M u s i c

During speech, human vocal cords tend to vibrate within a much smaller range that they would while singing. How is it then possible to distinguish the sound of one vowel from another? English is not a tonal language (unlike Chinese and many African languages). There is very little difference in the fundamental frequency of the vocal cords for English speakers during a declarative sentence. (Interrogative sentences rise in pitch near the end. Don't they?) Vocal cords don't vibrate with just one frequency, but with all the harmonic frequencies. Different arrangements of the parts of the mouth (teeth, lips, front and back of tongue, etc.) favor different harmonics in a complicated manner. This amplifies some of the frequencies and de-amplifies others. This makes "EE" sound like "EE" and "OO" sound like "OO".