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Chapter 15: Wave Motion

Chapter 15: Wave Motion. 15-9 Standing Waves; Resonance.

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Chapter 15: Wave Motion

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  1. Chapter 15: Wave Motion

  2. 15-9 Standing Waves; Resonance Standing wavesoccur when both ends of a string are fixed.In that case, only waves which are motionlessat the ends of the string can persist. There are nodes,where the amplitude is always zero, and antinodes,where the amplitude varies from zero to the maximum value.

  3. 15-9 Standing Waves; Resonance Thefrequenciesof the standing waves on a particular string are calledresonant frequencies. They are also referred to as the fundamental and harmonics.

  4. 15-9 Standing Waves on a string Fundamental frequency • For a given string, the wave speed is a constant, v=√F/µ • Boundary Condition: Each end of the string must be a node • Therefore, only certain wavelengths will fit on the string

  5. Fundamental or first harmonic Second harmonic Third Harmonic

  6. 15-9 Standing Waves; Resonance Thewavelengthsandfrequencies (resonant frequencies)of standing waves are: and

  7. 15-9 Standing Waves; Resonance Example 15-8: Piano string. A piano string is 1.10 m long and has a mass of 9.00 g. (a) How much tension must the string be under if it is to vibrate at a fundamental frequency of 131 Hz? (b) What are the frequencies of the first four harmonics?

  8. 15-9 Standing Waves; Resonance Example 15-9: Wave forms. Two waves traveling in opposite directions on a string fixed at x = 0 are described by the functions D1 = (0.20 m)sin(2.0x – 4.0t) and D2 = (0.20m)sin(2.0x + 4.0t) (where x is in m, t is in s), and they produce a standing wave pattern. Determine (a) the function for the standing wave, (b) the maximum amplitude at x = 0.45 m, (c) where the other end is fixed (x > 0), (d) the maximum amplitude, and where it occurs.

  9. Problem 48 48. (II) The velocity of waves on a string is 96m/s If the frequency of standing waves is 445 Hz, how far apart are the two adjacent nodes?

  10. Problem 49 49. (II) If two successive harmonics of a vibrating string are 240 Hz and 320 Hz, what is the frequency of the fundamental?

  11. 15-10 Refraction If the wave enters a medium where the wave speedis different, it will be refracted—its wave fronts and rays will change direction. We can calculate the angleof refraction, which depends on bothwave speeds: Law of Refraction

  12. 15-10 Refraction Thelaw of refractionworks both ways—a wave going from aslowermedium to a fasterone would follow the red line in the other direction.

  13. 15-10 Refraction Example 15-10: Refraction of an earthquake wave. An earthquake P wave passes across a boundary in rock where its velocity increases from 6.5 km/s to 8.0 km/s. If it strikes this boundary at 30°, what is the angle of refraction?

  14. 15-11 Diffraction When waves encounter an obstacle, they bend around it, leaving a “shadow region.” This is calleddiffraction.

  15. 15-11 Diffraction The amount of diffractiondepends on the size of the obstacle compared to thewavelength. If the obstacle is muchsmallerthan the wavelength, the wave is barely affected (a). If the object is comparableto, or largerthan, the wavelength, diffraction is much more significant (b, c, d).

  16. Chapter 16: Sound

  17. 16-1 Characteristics of Sound: Sound https://www.youtube.com/watch?v=GkNJvZINSEY

  18. 16-1 Characteristics of Sound Sound is a longitudinal wave Loudness: related to intensity of the sound wave (energy transported by the wave per unit time across unit area) Pitch: related to frequency Audible range: about 20 Hz to 20,000 Hz; upper limit decreases with age Ultrasound: above 20,000 Hz at room temperature

  19. 16-1 Characteristics of Sound: Problem 3 3.(I) (a) Calculate the wavelengths in air at 20°C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. (b) What is the wavelength of a 15-MHz ultrasonic wave?

  20. 16-3 Intensity of Sound: Decibels The intensity of a wave is the energy transported per unit time across a unit area. The human ear can detect sounds with an intensity as low as 10-12 W/m2 and as high as 1 W/m2,(Watts/m2) Perceived loudness, however, is not proportional to the intensity.

  21. 16-3 Intensity of Sound: Decibels The loudness of a sound is much more closely related to the logarithm of the intensity. Sound level is measured in decibels (dB) and is defined as: Where I0 is taken to be the thresholdof hearing (Watts/m2): The unit of the sound level β is decibel (dB)

  22. Problem 8 8. (II) A person, with his ear to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 0.75 s apart. How far away did the impact occur? See Table 16–1.

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