University Physics: Waves and Electricity. Ch1 7 . Longitudinal Waves. Lecture 5. Dr.-Ing. Erwin Sitompul. http://zitompul.wordpress.com. 2014. Homework 4 : Two Speakers.
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Ch17. Longitudinal Waves
Dr.-Ing. Erwin Sitompul
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?
(a) What is the lowest frequency fmin,1 that gives minimum signal (destructive interference) at the listener’s ear?
(b) What is the second lowest frequency fmin,2 that gives minimum signal?
(c) What is the lowest frequency fmax,1 that gives maximum signal (constructive interference) at the listener’s ear?
(d) What is the lowest frequency fmax,1 that gives maximum signal (constructive interference) at the listener’s ear?
Amplitude modulation, depends on Δk/2 and Δω/2
Oscillating term, a traveling wave, depends on k and ω
The A string of a violin is not properly tuned. Beats at 4 per second are heard when the string is sounded together with a tuning fork that is oscillating accurately at concert A (440 Hz).
(a) What are the possible frequencies produced by the string?
(b) If the string is stretched a little bit more, beats at 5 per second are heard. Which of the possible frequencies are the the frequency of the string?
where v is the speed of sound through the air, vD is the detector’s speed relative to the air, and vS is the source’s speed relative to the air.
+ The detector moves toward the source
– The detector moves away from the source
– The source moves toward the detector
+ The source moves away from the detector
The figure indicates the directions of motion of a sound source and a detector for six situations in stationary air. For each situation, is the detected frequency greater than or less than the emitted frequency, or can’t we tell without more information about the actual speeds?
Need more information
A toy rocket flies with a velocity of 242 m/s toward a mast while emitting a roaring sound with frequency 1250 Hz. The sound velocity is 343 m/s.
(a) What is the frequency heard by an observer who is standing at the mast?
(b) A fraction of the soundwaves is reflected by the mast and propagates back to the rocket. What is the frequency detected by a detector mounted on the head of the rocket?
vsource = vsound
(Mach 1 - sound barrier)
(Mach 1.4 - supersonic)
An ambulance with a siren emitting a whine at 1600 Hz overtakes and passes a cyclist pedaling a bike at 8 m/s. After being passed, the cyclist hears a frequency of 1590 Hz.
(a) How fast is the ambulance moving?
(b) What frequency did the cyclist hear before being overtaken by the ambulance?
1. An iron bar produces sound with a frequency of 335 Hz when struck. When the iron bar is struck together with a steel bar, beats with a frequency of 5.5 Hz will be heard. A piece of thread is then tied to the iron bar and its frequency is lowered slightly. When struck at the same time again, both the iron and steel bars now produce a beat with frequency of 8.2 Hz.
(a) What is the frequency of the iron bar after the thread is tied to it?
(b) What is the frequency of the steel bar?
2. (a) A stationary observer hears a frequency of 560 Hz from an approaching car. After the car passes, the observed frequency is 460 Hz. What is the speed of the car? (speed of sound is air is 343 m/s.)
(b) Abat, moving at 5 m/s, is chasing a flying insect. If the bat emits a 40 kHz chirp and receives back an echo at 40.4 kHz, at what speed is the insect moving toward or away from the bat?