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An acoustic signal is composed of the first three harmonics of a wave of fundamental frequency 470 Hz. If these harmonics are described, in order, by cosine waves with amplitudes of 0.710, 0.170, and 0.790, what is the total amplitude of the signal at time 0.414 seconds? Assume the waves have phase angles ?n = 0.

An acoustic signal is composed of the first three harmonics of a wave of fundamental frequency 470 Hz. If these harmonics are described, in order, by cosine waves with amplitudes of 0.710, 0.170, and 0.790, what is the total amplitude of the signal at time 0.414 seconds? Assume the waves have phase angles ?n = 0.

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An acoustic signal is composed of the first three harmonics of a wave of fundamental frequency 470 Hz. If these harmonics are described, in order, by cosine waves with amplitudes of 0.710, 0.170, and 0.790, what is the total amplitude of the signal at time 0.414 seconds? Assume the waves have phase angles ?n = 0.

Expert Solution
Step 1

Given:

  • The fundamental frequency of signal is f0=470 Hz.
  • The amplitude of first wave is A1=0.710.
  • The amplitude of second wave is A2=0.170.
  • The amplitude of third wave is A3=0.790.
  • The time take by signal is t=0.414 s.

The formula to calculate the frequency of nth wave is,

fn=nf0

Here, fn is the frequency of nth wave, n is the number of wave and f0 is the fundamental frequency.

Substitute the known values in the formula to calculate the frequency of first wave.

f1=1470 Hz=470 Hz

Substitute the known values in the formula to calculate the frequency of second wave.

f2=2470 Hz=940 Hz

Substitute the known values in the formula to calculate the frequency of third wave.

f3=3470 Hz=1410 Hz

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