Problem #11: By how many decibels do you reduce the sound intensity level due to a source ofsound if you quadruple your distance from it? Assume that the waves expand spherically.

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Answered: Problem #11: By how many decibels do…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter14: Sound

Section: Chapter Questions

Problem 22P: An outside loudspeaker (considered a small source) emits sound waves with a power output of 100 W....

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Consider two wave functions that differ only by a phase shift, y1(x,t)=Acos(kxt) and y2(x,t)=Acos(kxt+) . Use the trigonometric cosu+cosv=2cos(uv2)cos(u+v2) and cos()=cos() to find a wave equation for the wave resulting from the superposition of the two waves. Does the resulting wave function come as a surprise to you?
Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string producing a standing wave. The linear mass density of the string is =0.075 kg/m and the tension in the string is FT=5.00 N. The time interval between instances of total destructive interference is t=0.13 s. What is the wavelength of the waves?
The speaker system at an open-air rock concert forms a ring around the entire circular stage and delivers 50,000 W of power output. Assume the sound radiates in all directions equally as if it were generated by an isotropic point source and assume the sound energy is not absorbed by air. a. At what distance is the sound from the speakers barely audible? Note that your answer will be far too large since the model we are using for sound level ignores the power absorbed by the medium (air). How does your answer compare to the radius of the Earth? b. What is the closest distance audience members can be to the speakers if the sound is not to be painful to their ears?
Consider two wave functions y1(x,t)=Asin(kxt) and y2(x,t)=Asin(kx+t+) . What is the wave function resulting from the interference of the two wave? (Hint: sin()=sincoscossin and =2+2 .)
Suppose that the sound level from a source is 75 dB and then drops to 52 dB, with a frequency of 600 Hz. Determine the (a) initial and (b) final sound intensities and the (c) initial and (d) final sound wave amplitudes. The air temperature is TC=24.00C and the air density is =1.184kg/m3 .
Consider two sinusoidal sine waves traveling along a string, modeled as y1(x,t)=0.3msin(4m1x+3s1t+3) and y2(x,t)=0.6msin(8m1x6s1t) . What is the height of the resultant wave formed by the interference of the two waves at the position x=1.0 m at time t=3.0 s?
Two identical loudspeakers 10.0 m apart are driven by the same oscillator with a frequency of f = 21.5 Hz (Fig. P17.6) in an area where the speed of sound is 344 m/s. (a) Show that a receiver at point A records a minimum in sound intensity from the two speakers. (b) If the receiver is moved in the plane of the speakers, show that the path it should take so that the intensity remains at a minimum is along the hyperbola 9x2 16y2 = 144 (shown in red-brown in Fig. P17.6). (c) Can the receiver remain at a minimum and move very far away from the two sources? If so, determine the limiting form of the path it must take. If not, explain how far it can go. Figure P17.6
(a) What is the speed of sound in a medium where a 100kHz frequency produces a 5.96cm wavelength? (b) Which substance in Table 17.1 is this likely to be?
Two speakers, facing each other and separated by a distance d, each emit a pure tone of the same amplitude A with frequency f. The speed of each of the sound waves is vs. A listener stands between the speakers, a distance x from one of the speakers. a. What frequencies would cause a dead spot (complete destructive interference) at the listeners position? b. If the speakers are separated by 5.00 m with the listener 2.00 m from one of the speakers, what is the lowest frequency for which there is a dead spot? The speed of sound in air is 343 m/s.
Consider two wave functions, y2(x,t)=2.00msin(2m1x3s1t) and y2(x,t)=2.00msin(2m1x3s1t+6) . (a) Verifythat yR=2Acos(2)sin(kxt+2) is the solution forthe wave that results from a superposition of the two waves.Make a column for x,y1,y2,y1+y2 , and yR=2Acos(2)sin(kxt+2) . Plot four waves as a function of position where the range of x is from 0 to 12 m.
An outside loudspeaker (considered a small source) emits sound waves with a power output of 100 W. (a) Find the intensity 10.0 m from the source. (b) Find the intensity level in decibels at that distance. (c) At what distance would you experience the sound at the threshold of pain, 120 dB?
A trumpet creates a sound intensity level of 1.15 102 dB at a distance of 1.00 m. (a) What is the sound intensity of a trumpet at this distance? (b) What is the sound intensity of five trumpets at this distance? (c) Find the sound intensity of five trumpets at the location of the first row of an audience, 8.00 m away, assuming, for simplicity, the sound energy propagates uniformly in all directions. (d) Calculate the decibel level of the five trumpets in the first row. (e) If the trumpets are being played in an outdoor auditorium, how far away, in theory, can their combined sound be heard? (f) In practice such a sound could not be heard once the listener was 2-3 km away. Why cant the sound be heard at the distance found in part (e)? Hint: In a very quiet room the ambient sound intensity level is about 30 dB.

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Problem #11: By how many decibels do you reduce the sound intensity level due to a source of sound if you quadruple your distance from it? Assume that the waves expand spherically.