Read Waveforms: Amplitude, Period, Frequency, Phase & Midline

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| Questions: 20 | Updated: Nov 10, 2025
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1) A sound wave is modeled by y(t) = 0.6 sin(4π t)… What is the frequency?

Explanation

Standard form: y = A sin(2π f t) ⇒ 2π f = 4π ⇒ f = 2. Hence, 2 Hz.

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About This Quiz
Read Waveforms: Amplitude, Period, Frequency, Phase & Midline - Quiz

Learn how sound and light waves behave by identifying key features such as amplitude, frequency, period, and phase shift. You will interpret equations and graphs to find maximum and minimum values, locate the midline, and understand how changes in equations affect wave properties. This quiz helps you recognize how mathematical... see morewave models describe sound and light behavior in real life. see less

2)
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2) I(x) = 3 cos(πx) + 2… What is the period?

Explanation

For cos(Bx): T = 2π/B = 2π/π = 2 (same x-units). Hence, 2 μs.

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3) P(t) = −5 sin(20 t) + 1… What is the midline?

Explanation

General A sin(⋯)+D has midline y = D. Here D = 1. Hence, y = 1.

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4) L(t) = A cos(Bt − π/2) + D with amplitude 4, period 10 ns. Which is correct?

Explanation

Period T = 2π/B = 10 ⇒ B = 2π/10. Amplitude = 4. Hence, option B.

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5) Microphone: max 0.8 V, min −0.2 V… amplitude & midline?

Explanation

Amplitude = (max−min)/2 = (0.8−(−0.2))/2 = 0.5. Midline = (0.8+(−0.2))/2 = 0.3. Hence, 0.5 and 0.3.

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6) Y(x) = 2 sin(3x − π). Which is true?

Explanation

T = 2π/3. 3x−π = 3(x−π/3) ⇒ shift right π/3. Hence, A.

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7) Dimmer: midline 10, amplitude 3, frequency 5 Hz. Model?

Explanation

f = 5 ⇒ ω = 2πf = 10π. Add midline +10, amplitude 3. Hence, A.

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8) Y(t) = −1.5 cos(8π t) (mm). Period?

Explanation

T = 2π/ω = 2π/(8π) = 1/4 s. Hence, 1/4 s.

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9) Cosine wave: midline 2, max 7, min −3. Equation (no shift)?

Explanation

Amplitude = (7−(−3))/2 = 5; midline = 2 ⇒ y = 2 + 5 cos x. Hence, A.

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10) Y(t) = A sin(Bt + C) has period 0.02 s. Which is true?

Explanation

T = 2π/B = 0.02 ⇒ B = 2π/0.02 = 100π. Hence, 100π.

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11) B(t) = 6 − 4 sin(40π t). Amplitude & frequency?

Explanation

Amplitude = 4. ω = 40π ⇒ f = ω/2π = 20 Hz. Hence, 4 and 20 Hz.

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12) Midline y = −1, amplitude 2. Max at t = 0 with value 1. Which model?

Explanation

At t=0: 2·cos(0) − 1 = 1 (a maximum). Hence, 2 cos(ωt) − 1.

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13) A(t) = 2 + 1.5 cos(0.4π t). Modulation period?

Explanation

T = 2π/(0.4π) = 5 s. Hence, 5 s.

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14) Y(x) = 0.02 sin(2πx/5 − π/2)… Wavelength?

Explanation

Form sin(2πx/λ − …) ⇒ λ = 5 m. Hence, 5 m.

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15) S(t) = A sin(2π·440 t). Period?

Explanation

f = 440 ⇒ T = 1/f = 1/440 s. Hence, 1/440 s.

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16) Y(t) = 3 + 2 sin(6t − π/2). At t = 0, what is y?

Explanation

y(0) = 3 + 2 sin(−π/2) = 3 − 2 = 1. Hence, 1.

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17) Sinusoid: amplitude 7, midline −2, period π. Which equation?

Explanation

Period π ⇒ B = 2 (since 2π/B = π). Hence, y = 7 sin(2x) − 2.

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18) Y(t) = 1.2 cos(12π t) + 0.3 sin(12π t). Fundamental period?

Explanation

ω = 12π ⇒ f = 6 ⇒ T = 1/6 s. Hence, 1/6 s.

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19) B(t) = 8 + 3 cos(πt/2). Frequency?

Explanation

ω = π/2 ⇒ f = ω/2π = 1/4 Hz. Hence, 1/4 Hz.

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20) I(x) = 5 + 4 cos(6x − π/3). First maximum right of x = 0?

Explanation

Max when 6x − π/3 = 2πk. Smallest x>0: 6x = π/3 ⇒ x = π/18. Hence, π/18.

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A sound wave is modeled by y(t) = 0.6 sin(4π t)… What is the...
I(x) = 3 cos(πx) + 2… What is the period?
P(t) = −5 sin(20 t) + 1… What is the midline?
L(t) = A cos(Bt − π/2) + D with amplitude 4, period 10 ns. Which is...
Microphone: max 0.8 V, min −0.2 V… amplitude & midline?
Y(x) = 2 sin(3x − π). Which is true?
Dimmer: midline 10, amplitude 3, frequency 5 Hz. Model?
Y(t) = −1.5 cos(8π t) (mm). Period?
Cosine wave: midline 2, max 7, min −3. Equation (no shift)?
Y(t) = A sin(Bt + C) has period 0.02 s. Which is true?
B(t) = 6 − 4 sin(40π t). Amplitude & frequency?
Midline y = −1, amplitude 2. Max at t = 0 with value 1. Which model?
A(t) = 2 + 1.5 cos(0.4π t). Modulation period?
Y(x) = 0.02 sin(2πx/5 − π/2)… Wavelength?
S(t) = A sin(2π·440 t). Period?
Y(t) = 3 + 2 sin(6t − π/2). At t = 0, what is y?
Sinusoid: amplitude 7, midline −2, period π. Which equation?
Y(t) = 1.2 cos(12π t) + 0.3 sin(12π t). Fundamental period?
B(t) = 8 + 3 cos(πt/2). Frequency?
I(x) = 5 + 4 cos(6x − π/3). First maximum right of x = 0?
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