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You listen to music in a noisy environment (loud rumbling of an aircraft), resulting in the signal f(t) in figure 1. To hear the music better, you turn on the canceling noise option of your fancy headphones. The headphone performs the Fourier transform shown in figure 2, filters out the small amplitude components, and sends the filtered sound of figure 3 to your ear. (a) What are the principal frequencies of the unfiltered signal? (b) Write a function f(t) that represents the filtered sound. (c) The human ear associates the pitch of a note to the lowest frequency of a periodic signal. What is that frequency: According to the Fourier transform in figure 2. According to the filtered signal shown in figure 3. Use this information to explain how to produce a low pitch sound when your speakers can generate only frequencies higher than 100Hz. Sound = music + random noise Fourier transform of sound = music + noise Filtered Sound = music (1)4 4 2 0 10 20 30 40 50 60 t(milliseconds) 70 Figure 1 0.8 0.6- 0.4- 0.2 f(t) 3 50 100 150 200 250 300 0 10 20 f(Hz) Figure 2 им 30 40 t (milliseconds) Figure 3 50 60 70

You listen to music in a noisy environment (loud rumbling of an aircraft), resulting in the signal f(t) in figure 1. To hear the music better, you turn on the canceling noise option of your fancy headphones. The headphone performs the Fourier transform shown in figure 2, filters out the small amplitude components, and sends the filtered sound of figure 3 to your ear. (a) What are the principal frequencies of the unfiltered signal? (b) Write a function f(t) that represents the filtered sound. (c) The human ear associates the pitch of a note to the lowest frequency of a periodic signal. What is that frequency: According to the Fourier transform in figure 2. According to the filtered signal shown in figure 3. Use this information to explain how to produce a low pitch sound when your speakers can generate only frequencies higher than 100Hz. Sound = music + random noise Fourier transform of sound = music + noise Filtered Sound = music (1)4 4 2 0 10 20 30 40 50 60 t(milliseconds) 70 Figure 1 0.8 0.6- 0.4- 0.2 f(t) 3 50 100 150 200 250 300 0 10 20 f(Hz) Figure 2 им 30 40 t (milliseconds) Figure 3 50 60 70

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter17: Sound
Section: Chapter Questions
Problem 30P: Consider a sound wave moving through the air modeled with the equation...
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You listen to music in a noisy environment (loud rumbling of an aircraft), resulting in the signal f(t) in figure 1. To hear the music better, you turn on the canceling noise option of your fancy headphones. The headphone performs the Fourier transform shown in figure 2, filters out the small amplitude components, and sends the filtered sound of figure 3 to your ear. (a) What are the principal frequencies of the unfiltered signal? (b) Write a function f(t) that represents the filtered sound. (c) The human ear associates the pitch of a note to the lowest frequency of a periodic signal. What is that frequency: According to the Fourier transform in figure 2. According to the filtered signal shown in figure 3. Use this information to explain how to produce a low pitch sound when your speakers can generate only frequencies higher than 100Hz. Sound = music + random noise Fourier transform of sound = music + noise Filtered Sound = music (1)4 4 2 0 10 20 30 40 50 60 t(milliseconds) 70 Figure 1 0.8 0.6- 0.4- 0.2 f(t) 3 50 100 150 200 250 300 0 10 20 f(Hz) Figure 2 им 30 40 t (milliseconds) Figure 3 50 60 70
Transcribed Image Text:You listen to music in a noisy environment (loud rumbling of an aircraft), resulting in the signal f(t) in figure 1. To hear the music better, you turn on the canceling noise option of your fancy headphones. The headphone performs the Fourier transform shown in figure 2, filters out the small amplitude components, and sends the filtered sound of figure 3 to your ear. (a) What are the principal frequencies of the unfiltered signal? (b) Write a function f(t) that represents the filtered sound. (c) The human ear associates the pitch of a note to the lowest frequency of a periodic signal. What is that frequency: According to the Fourier transform in figure 2. According to the filtered signal shown in figure 3. Use this information to explain how to produce a low pitch sound when your speakers can generate only frequencies higher than 100Hz. Sound = music + random noise Fourier transform of sound = music + noise Filtered Sound = music (1)4 4 2 0 10 20 30 40 50 60 t(milliseconds) 70 Figure 1 0.8 0.6- 0.4- 0.2 f(t) 3 50 100 150 200 250 300 0 10 20 f(Hz) Figure 2 им 30 40 t (milliseconds) Figure 3 50 60 70
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