Example 6 In AM (Amplitude Modulated) radio, a carrier wave with a high frequency is used to transmit music or other signals by applying the to-be-transmitted signal as the amplitude of the carrier signal. A musical note with frequency 110 Hz (Hertz = cycles per second) is to be carried on a wave with frequency of 2 KHz (KiloHertz = thousands of cycles per second). If the musical wave has an amplitude of 3, write a function describing the broadcast wave. Show solution Solution The carrier wave, with a frequency of 2000 cycles per second, would have period of a second, giving an equation of the form sin(4000πt). Our choice of a sine function here was arbitrary - it would have worked just was well to use a cosine. 1 2000 1 The musical tone, with a frequency of 110 cycles per second, would have a period of of a second. 110 With an amplitude of 3, this would correspond to a function of the form 3 sin (220πt). Again our choice of using a sine function is arbitrary. The musical wave is acting as the amplitude of the carrier wave, so we will multiply the musical tone's function by the carrier wave function, resulting in the function f(t) = 3 sin(220πt) sin(4000ft) f(t) 3 NW 6.53 t

Example 6 In AM (Amplitude Modulated) radio, a carrier wave with a high frequency is used to transmit music or other signals by applying the to-be-transmitted signal as the amplitude of the carrier signal. A musical note with frequency 110 Hz (Hertz = cycles per second) is to be carried on a wave with frequency of 2 KHz (KiloHertz = thousands of cycles per second). If the musical wave has an amplitude of 3, write a function describing the broadcast wave. Show solution Solution The carrier wave, with a frequency of 2000 cycles per second, would have period of a second, giving an equation of the form sin(4000πt). Our choice of a sine function here was arbitrary - it would have worked just was well to use a cosine. 1 2000 1 The musical tone, with a frequency of 110 cycles per second, would have a period of of a second. 110 With an amplitude of 3, this would correspond to a function of the form 3 sin (220πt). Again our choice of using a sine function is arbitrary. The musical wave is acting as the amplitude of the carrier wave, so we will multiply the musical tone's function by the carrier wave function, resulting in the function f(t) = 3 sin(220πt) sin(4000ft) f(t) 3 NW 6.53 t

Inquiry into Physics

8th Edition

ISBN:9781337515863

Author:Ostdiek

Publisher:Ostdiek

Chapter6: Waves And Sound

Section: Chapter Questions

Problem 5C: An entrepreneur decides to invent and market a device that will fool the Doppler radar units used to...

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