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In the figure, two speakers separated by distance d₁ = 1.90 m are in phase. You are standing 3.20 m directly in front of one speaker. Each speaker has an output power of 1.70 W. Because the speakers are at different distances, there will be frequencies at which the sound from the speakers interferes destructively. But because the speakers are at different distances, the sound intensities will not be the same, so the destructive interference will not be complete. We want to find the sound level when there is destructive interference. Use 343 m/s for the speed of sound in air. d₁ Speakers do Listener (a) What is the lowest frequency that gives minimum signal (destructive interference) at your ear? 131.92 × Hz (b) What is the second lowest frequency that gives minimum signal? 395.84 × Hz (c) What is the intensity from the near speaker? (note: keep 6 significant figures or rounding may screw up your answer to part f) .037396 × W/m2 (d) What is the sound level from the near speaker? 105.74 dB (e) What is the intensity from the far speaker? (note: keep 6 sigfigs) .013195 × W/m2 (f) What is the combined intensity during destructive interference? Because the sources are coherent, amplitudes add but intensities do not. .006162 × W/m2 Confused? Click here for a video explaining part f and coherent vs incoherent waves (9.5 minutes). (g) What is the sound level during destructive interference? 97.91 × dB

In the figure, two speakers separated by distance d₁ = 1.90 m are in phase. You are standing 3.20 m directly in front of one speaker. Each speaker has an output power of 1.70 W. Because the speakers are at different distances, there will be frequencies at which the sound from the speakers interferes destructively. But because the speakers are at different distances, the sound intensities will not be the same, so the destructive interference will not be complete. We want to find the sound level when there is destructive interference. Use 343 m/s for the speed of sound in air. d₁ Speakers do Listener (a) What is the lowest frequency that gives minimum signal (destructive interference) at your ear? 131.92 × Hz (b) What is the second lowest frequency that gives minimum signal? 395.84 × Hz (c) What is the intensity from the near speaker? (note: keep 6 significant figures or rounding may screw up your answer to part f) .037396 × W/m2 (d) What is the sound level from the near speaker? 105.74 dB (e) What is the intensity from the far speaker? (note: keep 6 sigfigs) .013195 × W/m2 (f) What is the combined intensity during destructive interference? Because the sources are coherent, amplitudes add but intensities do not. .006162 × W/m2 Confused? Click here for a video explaining part f and coherent vs incoherent waves (9.5 minutes). (g) What is the sound level during destructive interference? 97.91 × dB

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter27: Wave Optics
Section: Chapter Questions
Problem 19P
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In the figure, two speakers separated by distance d₁ = 1.90 m are in phase. You are standing 3.20 m directly in front of one speaker. Each speaker has an output power of 1.70 W. Because the speakers are at different distances, there will be frequencies at which the sound from the speakers interferes destructively. But because the speakers are at different distances, the sound intensities will not be the same, so the destructive interference will not be complete. We want to find the sound level when there is destructive interference. Use 343 m/s for the speed of sound in air. d₁ Speakers do Listener (a) What is the lowest frequency that gives minimum signal (destructive interference) at your ear? 131.92 × Hz (b) What is the second lowest frequency that gives minimum signal? 395.84 × Hz (c) What is the intensity from the near speaker? (note: keep 6 significant figures or rounding may screw up your answer to part f) .037396 × W/m2 (d) What is the sound level from the near speaker? 105.74 dB (e) What is the intensity from the far speaker? (note: keep 6 sigfigs) .013195 × W/m2 (f) What is the combined intensity during destructive interference? Because the sources are coherent, amplitudes add but intensities do not. .006162 × W/m2 Confused? Click here for a video explaining part f and coherent vs incoherent waves (9.5 minutes). (g) What is the sound level during destructive interference? 97.91 × dB
Transcribed Image Text:In the figure, two speakers separated by distance d₁ = 1.90 m are in phase. You are standing 3.20 m directly in front of one speaker. Each speaker has an output power of 1.70 W. Because the speakers are at different distances, there will be frequencies at which the sound from the speakers interferes destructively. But because the speakers are at different distances, the sound intensities will not be the same, so the destructive interference will not be complete. We want to find the sound level when there is destructive interference. Use 343 m/s for the speed of sound in air. d₁ Speakers do Listener (a) What is the lowest frequency that gives minimum signal (destructive interference) at your ear? 131.92 × Hz (b) What is the second lowest frequency that gives minimum signal? 395.84 × Hz (c) What is the intensity from the near speaker? (note: keep 6 significant figures or rounding may screw up your answer to part f) .037396 × W/m2 (d) What is the sound level from the near speaker? 105.74 dB (e) What is the intensity from the far speaker? (note: keep 6 sigfigs) .013195 × W/m2 (f) What is the combined intensity during destructive interference? Because the sources are coherent, amplitudes add but intensities do not. .006162 × W/m2 Confused? Click here for a video explaining part f and coherent vs incoherent waves (9.5 minutes). (g) What is the sound level during destructive interference? 97.91 × dB
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