Build Wave Models: From Specs to Sine/Cosine (and Back)

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| Questions: 20 | Updated: Nov 10, 2025
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1) I(t) = 12 + 3 cos(4πt). Maximum intensity?

Explanation

Max = midline + amplitude = 12 + 3 = 15. Hence, 15.

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About This Quiz
Build Wave Models: From Specs To Sine/Cosine (And Back) - Quiz

Practice writing and adjusting equations for sound and light waves. You will work with amplitude, frequency, and phase to model waves that match given conditions. This quiz focuses on translating real-world descriptions into mathematical models, comparing phase shifts, and understanding how changing one part of an equation affects the wave’s... see moremotion, speed, and appearance. see less

2)
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2) Period 0.008 s, amplitude 0.5. Which equation?

Explanation

T=0.008 ⇒ f=125 ⇒ ω=2πf=250π. Hence, B.

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3) Y = 4 sin(6x − 18t + π/3). Wavelength?

Explanation

k=6 ⇒ λ=2π/k = π/3. Hence, π/3.

Submit
4) Right shift by 0.2 s. New phase φ′?

Explanation

Right shift Δt ⇒ use (ωt − ωΔt + φ) ⇒ φ′ = φ − ωΔt. Hence, φ − 0.2ω.

Submit
5) Original s(t) = 0.2 sin(440π t). New: amplitude ×3, pitch 220→330 Hz.

Explanation

New A=0.6. New ω=2π·330=660π. Hence, A.

Submit
6) Y = 2 cos(8πt − 4πx). Wave speed magnitude?

Explanation

ω=8π, k=4π ⇒ v=ω/k=2. Hence, 2.

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7) Wavelength 5 mm, midline 20, amplitude 6, peak at x=0. Which fits?

Explanation

Peak at x=0 ⇒ cosine; use 2πx/λ. Hence, B.

Submit
8) S(t) = 1.5 sin(2π·440 t − π/6). Phase shift in time?

Explanation

Right shift = φ/ω = (π/6)/(2π·440) = 1/5280 s. Hence, C.

Submit
9) Y = 0.1 sin(10πx − 40πt). Which is true?

Explanation

k=10π ⇒ λ=2π/k=0.2 m. (Also f=20 Hz, v=4 m/s.) Hence, λ=0.2 m.

Submit
10) Need amplitude 2, frequency 3 Hz, left shift 0.1 s.

Explanation

f=3 ⇒ ω=6π. Left shift Δt ⇒ +ωΔt = +0.6π. Hence, C.

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11) Y = A sin(2πx/0.8 − 2πt/0.2). Speed?

Explanation

λ=0.8, T=0.2 ⇒ v=λ/T=4.0 m/s. Hence, 4.0.

Submit
12) Peaks at t = 1.2, 1.7, 2.2… Max = 5, midline = 1. Correct equation?

Explanation

Amplitude = 5−1=4; T=0.5 s ⇒ ω=4π. Phase shift to match peaks. Hence, B.

Submit
13) Light in glass v = 2.0×10^8 m/s, λ = 400 nm. Frequency?

Explanation

f = v/λ = 2e8 / 4e−7 = 5e14. Hence, 5.0×10^14 Hz.

Submit
14) Delay y(t) = sin(12π t) by 15 ms. Which works?

Explanation

Right shift Δt=0.015 s ⇒ subtract phase ωΔt = 12π·0.015 = 0.18π. Hence, A.

Submit
15) S(t) = 0.4 sin(8π t − π/3). Frequency?

Explanation

2π f = 8π ⇒ f = 4. Hence, 4 Hz.

Submit
16) λ = 600 nm, c = 3.0×10^8 m/s. Frequency?

Explanation

f = c/λ = 3e8 / 6e−7 = 5e14. Hence, 5.0×10^14 Hz.

Submit
17) Y = 3 cos(5x − 20t). Wave speed?

Explanation

v = ω/k = 20/5 = 4. Hence, 4.

Submit
18) Amplitude 6, period 3 s, midline −2.

Explanation

T=3 ⇒ ω=2π/3 ⇒ y=6 sin((2π/3)t)−2. Hence, D.

Submit
19) S1 = 2 sin(10t), s2 = 2 sin(10t + π/2). Which is true?

Explanation

Phase lead +π/2 ⇒ Δt = (π/2)/ω = T/4. Hence, s2 leads by T/4.

Submit
20) Y = A sin(kx − ωt), f = 50 Hz, v = 20 m/s. What is k?

Explanation

λ = v/f = 0.4 ⇒ k = 2π/λ = 5π rad/m. Hence, 5π.

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I(t) = 12 + 3 cos(4πt). Maximum intensity?
Period 0.008 s, amplitude 0.5. Which equation?
Y = 4 sin(6x − 18t + π/3). Wavelength?
Right shift by 0.2 s. New phase φ′?
Original s(t) = 0.2 sin(440π t). New: amplitude ×3, pitch 220→330...
Y = 2 cos(8πt − 4πx). Wave speed magnitude?
Wavelength 5 mm, midline 20, amplitude 6, peak at x=0. Which fits?
S(t) = 1.5 sin(2π·440 t − π/6). Phase shift in time?
Y = 0.1 sin(10πx − 40πt). Which is true?
Need amplitude 2, frequency 3 Hz, left shift 0.1 s.
Y = A sin(2πx/0.8 − 2πt/0.2). Speed?
Peaks at t = 1.2, 1.7, 2.2… Max = 5, midline = 1. Correct equation?
Light in glass v = 2.0×10^8 m/s, λ = 400 nm. Frequency?
Delay y(t) = sin(12π t) by 15 ms. Which works?
S(t) = 0.4 sin(8π t − π/3). Frequency?
λ = 600 nm, c = 3.0×10^8 m/s. Frequency?
Y = 3 cos(5x − 20t). Wave speed?
Amplitude 6, period 3 s, midline −2.
S1 = 2 sin(10t), s2 = 2 sin(10t + π/2). Which is true?
Y = A sin(kx − ωt), f = 50 Hz, v = 20 m/s. What is k?
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