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Ch14.1 – Waves

Ch14.1 – Waves. Wave – rhythmic disturbance, carries energy through matter or space. Transverse wave – wave vibrates perpendicular to the direction of travel -like a rope. Longitudinal wave (compression) – wave vibrates parallel to the motion of the wave, like a slinky.

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Ch14.1 – Waves

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  1. Ch14.1 – Waves Wave – rhythmic disturbance, carries energy through matter or space. Transverse wave – wave vibrates perpendicular to the direction of travel -like a rope. Longitudinal wave (compression) – wave vibrates parallel to the motion of the wave, like a slinky.

  2. Formulas: v = λ∙ f f = 1/T Freq units: Waves/sec (Hertz) Period units: sec/wave frequency velocity wavelength Period (Time it takes for one wave to pass) freq (# of waves per second)

  3. Ch14.1 – Waves Wave – rhythmic disturbance, carries energy through matter or space. Transverse wave – wave vibrates perpendicular to the direction of travel - like a rope. Longitudinal wave (compression) – wave vibrates parallel to the motion of the wave, like a slinky. Formulas: v = λ∙ f f = 1/T Freq units: Waves/sec (Hertz) Period units: sec/wave Wavelength, (λ) crest Amplitude trough frequency velocity wavelength Period (Time it takes for one wave to pass) Freq (# of waves per second)

  4. Ex1) A sound wave has a frequency of 262 Hz and a wavelength measured at 1.29 m. a) What is the speed of the wave? b) How long will it take the wave to travel the length of a football field, 91.4m? c) What is the period of the wave? HW#1) A sound wave produced by a clock chime is heard 515 m away 1.50 s later. a. What is the speed of sound of the clock’s chime in air? b. The sound wave has a frequency of 436 Hz. What is its period? c. What is its wavelength?

  5. Ex1) A sound wave has a frequency of f = 262 Hz and a wavelength measured at λ = 1.29 m. a) What is the speed of the wave? b) How long will it take the wave to travel the length of a football field, 91.4m? c) What is the period of the wave? v=λ∙f =(1.29m)(2621/sec) =338m/s d = v∙ t t = d/v = 91.4m/338m/s = .27sec T=? T=1/f = 1/2621/sec = .004sec HW#1) A sound wave produced by a clock chime is heard 515 m away 1.50 s later. a. What is the speed of sound of the clock’s chime in air? b. The sound wave has a frequency of 436 Hz. What is its period? c. What is its wavelength? (v = λ∙f) or (v = d/t)? v = 515m/1.5sec = 343m/s T = ? T = 1/f = 1/4361/sec = .002sec v = λ∙ f λ= v/f = 343m/s/436 1/sec = .8m

  6. HW#7) A periodic longitudinal wave that has a frequency of 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave?

  7. HW#7) A periodic longitudinal wave that has a frequency of 20.0 Hz travels along a coil spring. If the distance between successive compressions is .400 m, what is the speed of the wave? f = 20.0 Hz v = λ∙ f = (.4m) (20 1/sec) = 8 m/s λ = .4m v =

  8. CH14 HW #1 1–7 In class A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later. a. What is the speed of sound of the hiker’s voice in air? b. The wavelength of the sound is .750 m. What is its frequency? c. What is the period of the wave? 3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency?

  9. CH14 HW #1 1–7 In class A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later. a. What is the speed of sound of the hiker’s voice in air? b. The wavelength of the sound is .750 m. What is its frequency? c. What is the period of the wave? 3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency? v = d/t = 685m/2s = 342.5m/s (v = λ∙ f) f = v/λ = 342.5m/s/.75m = 456.7 Hz T = 1/f = 1/456.7s-1 = .002s

  10. CH14 HW #1 1–7 In class A hiker shouts toward a vertical cliff 685 miles away. The echo is heard 4.00 sec later. a. What is the speed of sound of the hiker’s voice in air? b. The wavelength of the sound is .750 m. What is its frequency? c. What is the period of the wave? 3. If you want to increase the wavelength of waves in a rope should you shake it at a higher or lower frequency? Speed determined medium! (v = λ∙ f) v = d/t = 685m/2s = 342.5m/s (v = λ∙ f) f = v/λ = 342.5m/s/.75m = 456.7 Hz T = 1/f = 1/456.7s-1 = .002s Shake Fast : (Higher frequency) shorter wavelength Shake slow (Low freq) Longer wavelength

  11. 4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m? 5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength? 6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? 7. In class f = 5 waves/.1 sec = 50 Hz λ = 1.2cm = .012m

  12. 4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m? 5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength? 6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? 7. In class v = λ∙ f = (.6m)(2.5s-1) = 1.5 m/s f = 5 waves/.1 sec = 50 Hz λ = 1.2cm = .012m

  13. 4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m? 5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength? 6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? 7. In class v = λ∙ f = (.6m)(2.5s-1) = 1.5 m/s λ = v/f = 15.0m/s / 5.0s-1 = 3m f = 5 waves/.1 sec = 50 Hz λ = 1.2cm = .012m

  14. 4. What is the speed of a periodic wave disturbance that has a frequency of 2.50 Hz and a wavelength of .600 m? 5. The speed of a transverse wave in a string is 15.0 m/s. If a source produces a disturbance that has a frequency of 5.00 Hz, what is its wavelength? 6. Five pulses are generated every .100 s in a tank of water. What is the speed of propagation of the wave if the wavelength of the surface wave is 1.20 cm? 7. In class v = λ∙ f = (.6m)(2.5s-1) = 1.5 m/s λ = v/f = 15.0m/s / 5.0s-1 = 3m 1/sec f = 5 waves/.1 sec = 50 Hz λ = 1.2cm = .012m v = λ∙ f = (0.12m)(50s-1) = .6m/s

  15. Ch14.2 – Wave Behavior Incident wave – wave going in Reflected wave – wave going out. Reflection at a fixed boundary: Reflection at a moveable boundary: Passing from dense to less dense medium: Passing from less dense to more dense medium:

  16. Ch14.2 – Wave Behavior Incident wave – wave going in Reflected wave – wave going out. Reflection at a fixed boundary: Reflection at a moveable boundary: Passing from dense to less dense medium: Passing from less dense to more dense medium: Wave reflects 180o out of phase. Crest comes back as a trough. Wave reflects in phase. Crest comes back as crest. Part of wave continues upright, part reflects off interface upright. (Acts like moveable boundary.) Part of wave continues upright, part reflects off interface as trough. (Acts like fixed boundary.)

  17. Superposition of Waves Constructive interference – waves add energy Ex1) Ex2) Destructive Interference – waves cancel energy Ex3) Ex4) Ex5)

  18. Superposition of Waves Constructive interference – waves add energy Ex1) Ex2) Destructive Interference – waves cancel energy Ex3) Ex4) Ex5) Ch14 HW#2 8 – 11

  19. Lab14.1 – Waves - due next day - Ch14 HW#2 due at beginning of period

  20. Ch14 HW#2 8-11 8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted? 9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? 10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?

  21. Ch14 HW#2 8-11 8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted? Upright 9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? 10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?

  22. Ch14 HW#2 8-11 8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted? Upright 9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? Attached to wall 10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?

  23. Ch14 HW#2 8-11 8. A wave is sent along a spring. The spring is attached to a moveable pivot, as shown. What does the reflection look like, upright or inverted? Upright 9. A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the next room or is it lying loose on the floor? Attached to wall 10. A pulse is sent along a thin rope that is attached to a thick rope, which is tied to a wall, as shown. At point A part of the wave transmits though to the thin rope and part reflects back into the thick rope. What does each part look like?

  24. Sketch the resultant of each wave as the centers overlap on the dashed line: a) b) c)

  25. Sketch the resultant of each wave as the centers overlap on the dashed line: a) b) c)

  26. Ch15.1 – Sound Sound waves are longitudinal waves. - cause small pressure changes that are detected by ear. - transmit through solids and liquids the same way. - slower through denser materials, but faster if material is elastic. Speed of Sound Through Various Media Air (0oC) 331 m/s *Air (20oC) 343 m/s (HW#1) Water (25oC) 1493 m/s Sea Water(25oC) 1533 m/s Iron (25oC) 5130 m/s Rubber (25oC) 1550 m/s Ex1) A tuning fork produces a sound wave in air with a frequency of 261.6 Hz. At a room temp the speed of sound is 343 m/s. What is the wavelength?

  27. Ch15.1 – Sound Sound waves are longitudinal waves. - cause small pressure changes that are detected by ear. - transmit through solids and liquids the same way. - slower through denser materials, but faster if material is elastic. Speed of Sound Through Various Media Air (0oC) 331 m/s *Air (20oC) 343 m/s (HW#1) Water (25oC) 1493 m/s Sea Water(25oC) 1533 m/s Iron (25oC) 5130 m/s Rubber (25oC) 1550 m/s Ex1) A tuning fork produces a sound wave in air with a frequency of 261.6 Hz. At a room temp the speed of sound is 343 m/s. What is the wavelength? f = 261.6Hz v = 343 m/s λ = ?

  28. Loudness – perception of sound intensity Sound Level – measured in decibels - measures the range from the faintest heard sound to the loudest sounds. - 10 dB increase is perceived jet engine – 110db as being twice as loud. concert – - 50,000 people yelling for 90 minutes have the thermal energy ear damage – 70db equivalent of a cup of coffee. classroom – this class – faint sound – 0db (threshold of hearing) Pitch – related to frequency (High pitch = High Frequency)

  29. Doppler Effect – an apparent change in the pitch of a sound. (High pitch as approaches, low pitch as recedes.) Velocity of sound is a constant (determined by the medium!) Wavelengths get scrunched (small λ) Frequency goes up (v=λ.f) Wavelengths expand (big λ) Freq goes down. (v=λ.f) Ch15 HW#1

  30. Lab15.1 Speed of Sound with Cymbals - due tomorrow - Ch15 HW#1 due at beginning of period

  31. Ch15 HW#1 1 – 4 • Find the frequency of a sound wave moving in air at room temperature with a wavelength of .667m. • f = ? • v = 343 m/s • λ = 0.667m • 2. The human ear can detect sounds with frequencies between 20 Hz and 16,000 Hz. Find the largest and smallest wavelengths the ear can detect, assuming that the sound travels through air with a speed of 343 m/s. • f = 20Hz f = 16,000Hz • v = 343 m/s v = 343 m/s • λ = ? λ = ?

  32. Ch15 HW#1 1 – 4 • Find the frequency of a sound wave moving in air at room temperature with a wavelength of .667m. • f = ? • v = 343 m/s • λ = 0.667m • 2. The human ear can detect sounds with frequencies between 20 Hz and 16,000 Hz. Find the largest and smallest wavelengths the ear can detect, assuming that the sound travels through air with a speed of 343 m/s. • f = 20Hz f = 16,000Hz • v = 343 m/s v = 343 m/s • λ = ? λ = ?

  33. If you clap your hands and hear the echo from a distant wall 0.20 s later, how far away is the wall? • 4. What is the frequency of sound in air having a wavelength equal to the diameter of a 15 in. (38 cm) sub woofer speaker? • Of a 3.0 in (7.6 cm) tweeter? Use 343 m/s for speed of sound. • f = ? f = ? • v = 343 m/s v = 343 m/s • λ = 0.38m λ = 0.076m

  34. If you clap your hands and hear the echo from a distant wall 0.20 s later, how far away is the wall? • 4. What is the frequency of sound in air having a wavelength equal to the diameter of a 15 in. (38 cm) sub woofer speaker? • Of a 3.0 in (7.6 cm) tweeter? Use 343 m/s for speed of sound. • f = ? f = ? • v = 343 m/s v = 343 m/s • λ = 0.38m λ = 0.076m d = v.t = 343m/s. 0.10sec =

  35. Ch15.2 – Physics of Music Characteristic of 1 wavelength: crest trough Characteristic of 1 standing wave: reflection perfectly overlaps crest crest constructive destructive interference interference (antinodes) (nodes)

  36. Ch15.2 – Physics of Music Standing waves on strings – caused by constructive/destructive interference patterns that end on a node.

  37. L Fundamental frequency: ½λ fits L λ = 2L Anitnodes 1st harmonic: 1λ fits L λ = L Nodes 2nd harmonic: 1½ λ fits L λ = 2/3L String instruments have different lengths and thicknesses of strings that can vibrate at different frequencies (diff pitches).

  38. Ex1) A guitar string is 64 cm long. If the speed of sound is 343m/s, what is the lowest possible frequency the string can hold? Ex2) A 256 Hz “C” note is played on a piano. If the speed of sound is 343m/s , what is the length of the string? Ex3) A banjo has a string length of 80 cm. if v = 343m/s , what is the frequency of the 1st harmonic?

  39. Ex1) A guitar string is 64 cm long. If the speed of sound is 343m/s, what is the lowest possible frequency the string can hold? fund freq: ½λ=L ½λ = 0.64m λ = 1.28m Ex2) A 256 Hz “C” note is played on a piano. If the speed of sound is 343m/s , what is the length of the string? fund freq: ½λ=L f = 256Hz L = ½λ= 0.67m Ex3) A banjo has a string length of 80 cm. if v = 343m/s , what is the frequency of the 1st harmonic? 1st harmonic: 1λ fits L λ = 0.80m Ch15 HW#2 5 – 8

  40. Ch15 HW#2 5 – 8 • A mandolin string is 105 cm long. If it’s a cold day, the speed of sound is • 335 m/s, what is the lowest possible frequency the string can hold? • fund freq: • ½λ = L • ½λ = 1.05m • λ = 2.10m • A 512 Hz “C” note is played on a piano. If the speed of sound is 343 m/s, • what is the length of the string? • fund freq: • ½λ = L • f = 512Hz • 7. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the second harmonic? • 1½ λfits L • λ = 2/3 L • λ = 2/3(0.8m) • λ = 0.53m

  41. Ch15 HW#2 5 – 8 • A mandolin string is 105 cm long. If it’s a cold day, the speed of sound is • 335 m/s, what is the lowest possible frequency the string can hold? • fund freq: • ½λ = L • ½λ = 1.05m • λ = 2.10m • A 512 Hz “C” note is played on a piano. If the speed of sound is 343 m/s, • what is the length of the string? • fund freq: • ½λ = L • f = 512Hz • ½λ = L = • 7. A banjo has a string length of 80 cm. If v = 343 m/s, what is the frequency of the second harmonic? • 1½ λfits L • λ = 2/3 L • λ = 2/3(0.8m) • λ = 0.53m

  42. 8. A bass guitar has a string length of 95 cm. If v = 343 m/s, what is the frequency of the first harmonic? • Fund Freq • 1st harmonic • λ = L = 0.95m

  43. 8. A bass guitar has a string length of 95 cm. If v = 343 m/s, what is the frequency of the first harmonic? • Fund Freq • 1st harmonic • λ = L = 0.95m

  44. Ch15.3 – Waves in Pipes Reminder: standing wave: Closed Pipes – antinode at open end, node at closed end. Fundamental Freq: 1st Harmonic: Ex1) A 512 Hz is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound?

  45. Ch15.3 – Waves in Pipes Reminder: standing wave: Closed Pipes – antinode at open end, node at closed end. Fundamental Freq: 1st Harmonic: ¼ λ fits L ¾λ fits L λ = 4L λ = 4/3 L Ex1) A 512 Hz tuning fork is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound?

  46. Ch15.3 – Waves in Pipes Reminder: standing wave: Closed Pipes – antinode at open end, node at closed end. Fundamental Freq: 1st Harmonic: ¼ λ fits L ¾λ fits L λ = 4L λ = 4/3 L • Ex1) A 512 Hz tuning fork is held above a closed pipe 16 cm long when sound resonates. What is the speed of sound? • ¼ λ fits L v = λ.f • λ = 4(.16m) = (0.64m)(512 s-1) • λ = 0.64m = 328 m/s

  47. Spacings – resonance will occur again when the closed pipe is lengthened every 1/2λ. Ex2) A 392 Hz tuning fork resonates sound waves in closed pipes that are 21 cm long and 63 cm. What is the speed of sound?

  48. Spacings – resonance will occur again when the closed pipe is lengthened every 1/2λ. Ex2) A 392 Hz tuning fork resonates sound waves in closed pipes that are 21 cm long and 63 cm. What is the speed of sound? 21cm 63cm ½λ = (one football) = 63 – 21 = 42cm λ = 0.84m f = 392Hz v = λ.f = (0.84m)(392s-1) = 329 m/s

  49. Open Pipe – open at both ends (antinodes) HW#12) A bugle can be thought of as an open pipe as shown. If a bugle were straightened out, it would be 2.65 m long. If the speed of sound is 343 m/s, find the lowest frequency that is resonant in a bugle. Find the next higher-resonant frequency in the bugle.

  50. Open Pipe – open at both ends (antinodes) Fund freq: 1st harmonic: ½λ fits L λ fits L λ = 2L λ = L HW#12) A bugle can be thought of as an open pipe as shown. If a bugle were straightened out, it would be 2.65 m long. If the speed of sound is 343 m/s, find the lowest frequency that is resonant in a bugle. Find the next higher-resonant frequency in the bugle. ½λ = L λ = L Ch15 HW#3 9 – 13

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