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2. A microphone receives sound pressure u(t) and converts it into a voltage signal x(t). Consider the case when the input sound pressure is u(t) = −2 cos (wot + 717) + 3 sin (2wot - 17) - Answer the following questions. cos 3wot (a) What is the fundamental frequency? Which term is the second harmonics? (5) (b) Figure 2 shows the magnitude and phase of the frequency response function G(w) of the microphone from u(t) to x(t). Please note that the frequency axis is in a log scale, and its unit is rad/s not Hz. When wo 50 rad/s, what is G(w) (both in magnitude and phase) at wo, 2w0, and 3wo? (c) What is the voltage output x(t) of the microphone when wo = 50 rad/s? Which har- monics dominates the response x(t) and why? (d) Find the range of the fundamental frequency wo in order for the microphone to properly reproduce the sound pressure u(t). Explain why to justify your answer. 10 Frequency (rad's) m x(t) u(t) Figure 1: A mass-damper system ġ(1) v(t) Mechanical Deformation Piezo Charge Amplifer Figure 2: Frequency response function of a microphone Figure 3: A simple model for piezoelectric sensor

2. A microphone receives sound pressure u(t) and converts it into a voltage signal x(t). Consider the case when the input sound pressure is u(t) = −2 cos (wot + 717) + 3 sin (2wot - 17) - Answer the following questions. cos 3wot (a) What is the fundamental frequency? Which term is the second harmonics? (5) (b) Figure 2 shows the magnitude and phase of the frequency response function G(w) of the microphone from u(t) to x(t). Please note that the frequency axis is in a log scale, and its unit is rad/s not Hz. When wo 50 rad/s, what is G(w) (both in magnitude and phase) at wo, 2w0, and 3wo? (c) What is the voltage output x(t) of the microphone when wo = 50 rad/s? Which har- monics dominates the response x(t) and why? (d) Find the range of the fundamental frequency wo in order for the microphone to properly reproduce the sound pressure u(t). Explain why to justify your answer. 10 Frequency (rad's) m x(t) u(t) Figure 1: A mass-damper system ġ(1) v(t) Mechanical Deformation Piezo Charge Amplifer Figure 2: Frequency response function of a microphone Figure 3: A simple model for piezoelectric sensor

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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2. A microphone receives sound pressure u(t) and converts it into a voltage signal x(t). Consider the case when the input sound pressure is u(t) = −2 cos (wot + 717) + 3 sin (2wot - 17) - Answer the following questions. cos 3wot (a) What is the fundamental frequency? Which term is the second harmonics? (5) (b) Figure 2 shows the magnitude and phase of the frequency response function G(w) of the microphone from u(t) to x(t). Please note that the frequency axis is in a log scale, and its unit is rad/s not Hz. When wo 50 rad/s, what is G(w) (both in magnitude and phase) at wo, 2w0, and 3wo? (c) What is the voltage output x(t) of the microphone when wo = 50 rad/s? Which har- monics dominates the response x(t) and why? (d) Find the range of the fundamental frequency wo in order for the microphone to properly reproduce the sound pressure u(t). Explain why to justify your answer. 10 Frequency (rad's) m x(t) u(t) Figure 1: A mass-damper system ġ(1) v(t) Mechanical Deformation Piezo Charge Amplifer Figure 2: Frequency response function of a microphone Figure 3: A simple model for piezoelectric sensor
Transcribed Image Text:2. A microphone receives sound pressure u(t) and converts it into a voltage signal x(t). Consider the case when the input sound pressure is u(t) = −2 cos (wot + 717) + 3 sin (2wot - 17) - Answer the following questions. cos 3wot (a) What is the fundamental frequency? Which term is the second harmonics? (5) (b) Figure 2 shows the magnitude and phase of the frequency response function G(w) of the microphone from u(t) to x(t). Please note that the frequency axis is in a log scale, and its unit is rad/s not Hz. When wo 50 rad/s, what is G(w) (both in magnitude and phase) at wo, 2w0, and 3wo? (c) What is the voltage output x(t) of the microphone when wo = 50 rad/s? Which har- monics dominates the response x(t) and why? (d) Find the range of the fundamental frequency wo in order for the microphone to properly reproduce the sound pressure u(t). Explain why to justify your answer. 10 Frequency (rad's) m x(t) u(t) Figure 1: A mass-damper system ġ(1) v(t) Mechanical Deformation Piezo Charge Amplifer Figure 2: Frequency response function of a microphone Figure 3: A simple model for piezoelectric sensor
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