1. Lecture #28: Waves and Sound AP Physics B

2. wave direction What is a wave? A wave is a traveling disturbance. A wave carries energy from place to place. Transverse Waves Waves in which the disturbed medium moves perpendicularly to the direction of travel of the wave.

3. wavelength, rarefaction compression molecule Longitudinal Waves: A wave in which the disturbed medium moves parallel to the line of travel of the wave. The wave consists of a series of alternating compressed and stretched regions. Sound is a longitudinal wave.

4. wavelength, Sound is created by a vibrating object that disturbs an adjacent medium such as a liquid, gas, or solid. Sounds requires a medium in order for the wave to move from place to place. Sound can not exist in a vacuum.

5. Wavelength (λ) Wavelength (λ): Amplitude: Period (T): Frequency (f): The horizontal length of one cycle. The maximum displacement of a particle of the medium from the particle’s undisturbed position. The time required for a wave to complete one cycle. The # of cycles that are completed in one second. f = 1/T

6. v = λ. f The speed of a wave can be determined by knowing the wavelength and frequency of the wave. The speed of a wave is determined by the properties of the medium through which it travels. √ v = _____ F____ m/L Tension of String Linear density

7. When a wave reaches a medium that is different in density than its previous medium, the wave will be reflected. If the medium that it encounters is more dense than the previous medium the wave will be reflected in an INVERTED form. If the medium that it encounters is less dense than the previous medium the wave will be reflected in an UPRIGHT form.

8. As was stated earlier, when a wave reaches a medium that is of a different density, that wave will be partially reflected and partially transmitted. The amount of “change” in the medium determines the amount of reflection and transmission.

9. substancespeed (m/s) Gases Air (0 o C)331 Air (20 o C)343 CO 2 (0 o C)259 Oxygen (0 o C)316 Helium (0 o C)965 Liquids Chloroform (20 o C)1004 Ethanol (20 o C)1162 Mercury (20 o C)1450 Fresh Water (20 o C)1482 Sea Water (20 o C)1522 Solids Copper5010 Glass (pyrex)5640 Lead1960 Steel5960 The speed of a sound wave is determined by the properties of the medium through which it travels. In general, sound travels slowest in gases and fastest in solids.

10. B  P P x A C A:  P = 0; P = P 0 B:  P > 0; P = P max C:  P < 0; P = P min

11. sound waves take on the frequency of the vibrating object that produced them. Pure Tone:A sound with a single frequency. Younger people hear frequencies in the range of 20 to 20,000 Hz Infrasonic:Sound waves that have a frequency too low for people to hear. Ultrasonic:Sound waves that have a frequency too high for people to hear. Did You Know? As you grow older your ability to hear higher frequencies diminishes. Bats use ultrasonic sound waves to locate their prey (bugs).

12. Doppler Effect:The change in pitch or frequency of the sound detected by an observer because the sound source and the observer have different velocities with respect to the medium of the sound propagation. Example: Moving Sound Source Wavelengths decrease ahead of a moving sound source, causing frequencies to increase ahead of the source and decrease behind the source. λ ’ = λ- v s T λ ’ = λ+ v s T

13. Moving Observer: An observer moving toward a stationary source experiences a higher frequency. An observer moving away from a stationary source experiences a lower frequency.

14. The principle of linear superposition: When two or more waves are present simultaneously at the same place, the resultant wave is the sum of the individual waves. Constructive interference Destructive interference When two waves that are exactly in phase overlap. When two waves that are exactly out of phase overlap.

15. constructive interference occurs when a crests overlaps with another crest constructive interference occurs when a trough overlaps with another trough. a listener that experiences constructive interference will hear a louder sound.

16. destructive interference occurs when a trough overlaps with a crest a listener that experiences destructive interference will hear a quieter sound. a difference in path lengths that is an integer number (1,2,3,…) of wavelengths leads to constructive interference; a difference in path lengths that is a half-integer number (½, 1½, 2½, …) of wavelengths leads to destructive interference.

17. The overlapping of two sound waves produces interference effects in the shaded region. Constructive Interference Destructive Interference A listener at these points would hear a louder sound. A listener at these points would hear no sound.

18. Two in-phase loudspeakers, A and B, are separated by 3.20 m. A listener is stationed at point C, which is 2.40 m in front of speaker B. The triangle ABC is a right triangle. Both speakers are playing identical 214 Hz tones, and the speed of sound is 343 m/s. Does the listener hear a loud sound or no sound? Distance A C = √(3.20m) 2 + (2.40m) 2 =4.00 m v = λ. f λ= v/f = 343m/s = 214 Hz 1.60 m Difference in travel lengths: 4.00 m – 2.40 m = 1.60 m (The difference in path length is equal to 1 wavelength, therefore a louder sound will be heard due to constructive interference.)

19. If you send more than one wave pulse down a coil, there will be waves traveling in both directions, and the wave traveling down the coil will interfere with the reflected wave coming back. Usually there will be quite a jumble. But if you vibrate the cord at just the right frequency, the two traveling waves will interfere in such a way that a large-amplitude STANDING WAVE will be produced. It is called a “standing wave” because it doesn’t appear to be traveling. The coil simply oscillates up and down with a fixed pattern. The points of destructive interference, where the coil remains still, are called nodes: points of constructive interference, where the coil oscillates with maximum amplitude, are called antinodes.

21. L ½ λ Nodes and Antinodes always alternate. Nodes and Antinodes are equally spaced. The distance between successive nodes is equal to ½ λ. Standing waves can only form when the length of the string is a multiple of ½ λ. L = n(½ λ) Harmonic # λ= 2L n Solving for wavelength: Solving for frequency:From f=v/λ,f=nv 2L