University Physics: Waves and Electricity. Ch1 7 . Longitudinal Waves. Lecture 4. Dr.-Ing. Erwin Sitompul. http://zitompul.wordpress.com. 2013. Homework 3 : Standing Waves.
Ch17. Longitudinal Waves
Dr.-Ing. Erwin Sitompul
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?
(a) Identical except direction of travel ► standing waves:
(b) Distance between nodes:
(c) Transversal speed:
At x = 1.5 cm = 15 mm and t = 9/8 s = 3/160 min,
Fully constructive,arrive “in phase”
Fully destructive,arrive “out of phase”
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 undergofully constructive interference at P1
(b) What are the path length difference and type of interference at point P2?
The waves undergo fully destructive interference at P2
(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 6points where the interference is a fully constructive interference
An electric spark jumps along a straight line of length L = 10 m, emitting a pulse of sound that travels radially outward from the spark. (The spark is said to be a line source of sound.) The power of the emission is Ps = 1.6×104 W.
(a) What is the intensity I of the sound when it reaches a distance r = 12 m from the spark?
(b) At what time rate Pd is sound energy intercepted by an acoustic detector of area Ad = 2.0 cm2, aimed at the spark and located a distance r = 12 m from the spark?
Many veteran rockers suffer from acute hearing damage because of the high sound levels they endured for years while playing music near loudspeakers or listening to music on loud headphones.
Recently, many of them began wearing special earplugs to protect their hearing during performances.
If an earplug decreases the sound level of the sound waves by 20 dB, what is the ratio of the final intensity If of the waves to their initial intensity Ii?
Standing Waves in a Pipe
Pipe A, with length L, and pipe B, with length 2L, both have two open ends. Which harmonic of pipe B has the same frequency as the fundamental of pipe A?
Weak background noises from a room set up the fundamental standing wave in a cardboard tube of length L = 67.0 cm with two open ends. Assume that the speed of sound in the air within the tube is 343 m/s
(a) What frequency do you hear from the tube?
(b) If you jam your ear against one end of the tube, what fundamental frequency do you hear from the tube?
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?
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.
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?
Organ pipe C, with both ends open, has a fundamental frequency of 320 Hz. The fifth harmonic of organ pipe D, with one end open, has the same frequency as the third harmonic of pipe C. Determine the length of pipe C and pipe D if the speed of sound in air is 343 m/s.