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University Physics: Waves and Electricity

University Physics: Waves and Electricity. Ch1 7 . Longitudinal Waves. Lecture 4. Dr.-Ing. Erwin Sitompul. http://zitompul.wordpress.com. Homework 3 : Standing Waves.

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University Physics: Waves and Electricity

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  1. University Physics: Waves and Electricity Ch17. Longitudinal Waves Lecture 4 Dr.-Ing. Erwin Sitompul http://zitompul.wordpress.com

  2. Homework 3: Standing Waves Two identical waves (except for direction of travel) oscillate through a spring and yield a superposition according to the equation (a) What are the amplitude and speed of the two waves? (b) What is the distance between nodes? (c) What is the transverse speed of a particle of the string at the position x = 1.5 cm when t = 9/8 s?

  3. Solution of Homework 3 (a) Identical except direction of travel ► standing waves: (b) Distance between nodes:

  4. Solution of Homework 3 (c) Transversal speed: At x = 1.5 cm = 15 mm and t = 9/8 s = 3/160 min,

  5. Sound Waves • From previous chapter we know that mechanical waves are classified into transverse waves and longitudinal waves. • In this class, a sound wave is defined roughly as a longitudinal waves. • The figure above illustrates several ideas useful for the next discussions. • Point S represents a tiny sound source, called a point source. It emits sound waves in all directions. • Wavefronts are surfaces over which the oscillation due to the sound wave have the same value. • Rays are directed lines perpendicular to the wavefronts that indicate the direction of travel of the wavefronts.

  6. Sound Waves • As a longitudinal wave, sound wave travels through a medium (solid, liquid, or gas), involving oscillations parallel to the direction of wave travel. • When a sound wave moves in time, the displacement of air molecules, the pressure, and the density vary sinusoidally with the frequency of the vibrating source.

  7. Interference • Like transverse waves, sound waves can undergo interference. • Now we will consider, in particular, the interference between two identical sound waves traveling in the same direction. • Two point sources S1 and S2 emit sound waves that are in phase and of identical wavelength λ. • Thus, as the waves emerge from the sources, their displacements are always identical. • The waves travels through point P, with the distance L1 or L2 much greater than the distance between the sources, S1 and S2. • The two sources can be approximated to travel in the same direction at P.

  8. Interference • From the figure, the path L2 traveled by the wave from S2 is longer than the path L1 traveled by the wave from S1. • The difference in path lengths means that the waves may not be in phase at point P. • The phase difference Φat P depends on their path length difference, • The relation between phase difference to path length difference, as we recall from previous chapter, is:

  9. Interference • Fully constructive interference occurs when Φis zero, 2π, or any integer multiple of 2π. • Fully constructive interference • Fully destructive interference occur when Φis an odd multiple of π, • Fully destructive interference

  10. Interference Fully constructive,arrive “in phase” Fully destructive,arrive “out of phase”

  11. Example: Interference Two point sources S1 and S2, which are in phase and separated by distance D = 1.5λ, emit identical sound waves of wavelength λ. (a)What is the path length difference of the waves from S1 and S2 at point P1, which lies on the perpendicular bisector of distance D, at a distance greater that D from the sources? What type of interference occurs at P1? The waves undergo fully constructive interference at P1

  12. Example: Interference (b) What are the path length difference and type of interference at point P2? The waves undergo fully destructive interference at P2

  13. Example: Interference (c) The figure below shows a circle with a radius much greater than D, centered on the midpoint between sources S1 and S2. What is the number of points N around this circle at which the intereference is fully constructive? Using the symmetry, as we go around the circle, we will find 6 points where the interference is a fully constructive interference

  14. Homework 4: Two Speakers Two speakers separated by distance d1 = 2 m are in phase. A listener observes at distance d2 = 3.75 m directly in front of one speaker. Consider the full audible range for normal human hearing, 20 Hz to 20 kHz. Sound velocity is 343 m/s. What is the lowest frequency fmin,1 that gives minimum signal (destructive interference) at the listener’s ear? What is the second lowest frequency fmin,2 that gives minimum signal? What is the lowest frequency fmax,1 that gives maximum signal (constructive interference) at the listener’s ear? What is the highest frequency fmax,n that gives maximum signal?

  15. Homework 4: Other Two Speakers Two loudspeakers, A and B, are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 12 m to the right of speaker A. The frequency of the waves emitted by each speaker is 686 Hz. Sound velocity is 343 m/s. You are standing between the speakers, along the line connecting them, and are at a point of constructive interference. New How far must you walk toward speaker B to move to a point of destructive interference? How far must you walk toward speaker B to move to another point of constructive interference?

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