Review Transverse Wave on a String Slinky Waves SOUND WAVES

L 23 – Vibrations and Waves [3] Review

¾ resonance √ ¾ A wave is a disturbance that travels through ¾ clocks – pendulum √ ¾ springs √ something – solids, liquids or gases ¾ harmonic motion √ ¾ The disturbance moves because of the ¾ mechanical waves √ elastic nature of the material ¾ sound waves ¾ As the disturbance moves, the parts of the ¾ golden rule for waves ¾ musical instruments material (segment of string, air molecules) ¾ The Doppler effect execute harmonic motion (move up and z Doppler radar down or back and forth) z radar guns

transverse wave on a string Harmonic waves – keep jiggling the end of the string up and down

• jiggle the end of the string to create a disturbance • the disturbance moves down the string • as it passes, the string moves up and then down •the string motion in vertical but the wave moves in the horizontal (perpendicular) directionÎ transverse wave • this is a single pulse wave (non-repetitive) • the “wave” in the football stadium is a transverse wave

Slinky waves SOUND WAVES

• you can create a • longitudinal pressure longitudinal wave on disturbances in a gas a slinky • the air molecules • instead of jiggling the jiggle back and forth slinky up and down, you jiggle it in and out in the same direction as the wave • the coils of the slinky move along the same direction (horizontal) the diaphragm of the as the wave speaker moves in and out

1 Sound – a longitudinal wave The pressure waves make your eardrum vibrate

• we can only hear sounds between 30 Hz and 20,000 Hz • below 30 Hz is called infrasound • above 20,000 is called ultrasound • can you hear this?

• drop 1 pebble in pond every 4 seconds Top view of ripples on a pond • ripples travel away at speed v = 2 cm/s 8 cm 8 cm 8 cm TIME v pebble ripples 1 sec. #1

5 sec. #2 #1

9 sec. #3 #2 #1

13 sec. #4 #3 #2 #1 2 cm 10 cm 18 cm 26 cm

The golden rule for waves The golden rule for waves

• Notice that the ripples are all separated by • This last result was not a coincidence a distance of 8 cm this is called the • The wavelength = wave speed / frequency wavelength λ (Greek letter lambda) λ= v / f or Î v = λ×f • The frequency, f at which the waves are Wave speed = wavelength × frequency emitted (pebbles) is 1 per 4 seconds or • This applies to all waves Æ water waves, ¼ Hz or 0.25 Hz. [1 Hertz (Hz) = 1 per sec] waves on strings, sound, radio, light . . • This rule is important for understanding -1 • wavelength λ = 8 cm, frequency f = ¼ s how musical instruments work and v = 4 cm/s = 8 cm x ¼ s-1 = λ x f

2 Example: wave on a string Sound and Music

• SoundÆ pressure waves in a solid, liquid or gas

• The speed of soundÆ vs 2 cm 2 cm 2 cm • Air at 20 C: 343 m/s = 767 mph ≈ 1/5 mile/sec • A wave moves on a string at a speed of 4 cm/s • Water at 20 C: 1500 m/s • A snapshot of the motion reveals that the • copper: 5000 m/s wavelength(λ) is 2 cm, what is the frequency (ƒ)? • Depends on density and temperature •v = λ×ƒ, so ƒ = v ÷ λ = (4 cm/s ) / (2 cm) = 2 Hz

5 second rule for thunder and lightening

Why do I sound funny when Tuning forks make sound waves I breath helium? • Sound travels twice as fast in helium, • The vibration of the fork because Helium is lighter than air causes the air near it to vibrate • Remember the golden rule vs = λ×ƒ • The wavelength of the sound waves you • The size of the fork make with your voice is fixed by the size of determines the frequency your mouth and throat cavity. – bigger fork Æ lower f –smaller fork Æ higher f • Since λ is fixed and vs is higher in He, the frequencies of your sounds is twice as • It produces a pure pitchÆ high in helium! single frequency

Stringed instruments Vibration modes of a string

• Three types – Plucked: guitar, bass, harp, harpsichord NNA Fundamental mode Wavelength = 2 L – Bowed: violin, viola, cello, bass Frequency = fo – Struck: piano L • All use strings that are fixed at both ends A – Use different diameter strings (mass per unit N N A N length is different) First harmonic mode Wavelength = L

– The string tension is adjustable - tuning L Frequency = 2 fo

N = nodes, A = antinodes

3 Standing waves Vibration frequencies

• At the NODE positions, the string does not • In general, f = v / λ, where v is the move propagation speed of the string • At the ANTINODES the string moves up • The propagation speed depends on the and down harmonically diameter and tension • Only certain wavelengths can fit into the • Modes

distance L – Fundamental: fo = v / 2L

• The frequency is determined by the – First harmonic: f1 = v / L = 2 fo velocity and mode number (wavelength) • The effective length can be changed by the musician “fingering” the strings

Bowed instruments Organ pipes • The air pressure inside the • In violins, violas, cellos and basses, a bow made pipe can vibrate, in some of horse hair is used to excite the strings into places it is high and in other vibration places low • Each of these instruments are successively • Depending on the length of bigger (longer and heavier strings). the pipe, various resonant • The shorter strings make the high frequencies modes are excited, just like and the long strings make the low frequencies blowing across a pop bottle • Bowing excites many vibration modes • The long pipes make the low simultaneouslyÆ mixture of tones (richness) notes, the short pipes make the high notes

Beats – wave interference • Waves show a special property called interference • When two waves are combined together, the waves can add or subtract • We call this constructive and destructive interference • When a wave is launched on a string it can reflect back from the far end. The reflected wave can combine with the original wave to make a standing wave

4 Constructive interference Destructive interference

waves add to give 0 amplitude Waves add to double amplitude

Combining 2 waves of the same frequency Combining 2 waves of slightly different frequencies

Red + Blue

Red + Blue Beats

Room Acoustics The Doppler Effect • If a source of sound is moving toward you, you hear a higher frequency than when it • Destructive interference accounts for bad is at rest room acoustics • If a source of sound is moving away from you, you hear a lower frequency than • Sound that bounces off a wall can interfere when it is at rest destructively (cancel out) sound from the • You can hear this effect with sirens on fire speakers resulting in dead spots engines of train whistles • A similar effect occurs with light waves and radar waves

5 Doppler effect Æ Radar guns A science teacher demonstrating the Doppler effect

When radar waves bounce off a moving object (echo )the frequency of the reflected radar changes by an amount that depends on how fast the object is moving. The detector senses the frequency shift and translates this into a speed.

http://auto.howstuffworks.com/radar-detector1.htm

Once you see the cop, he’s got you!