Sound Wave Function Quiz: Writing Basic Sound Wave Function

1) Select all true statements for s(t)=2·sin(2π·50·t)+3.

Amplitude is 2

Period is 1/50 seconds

Midline is y=3

Frequency is 100 Hz

Maximum value is 5

Amplitude |A|=2; F=50 Hz so T=1/50 s; D=3 is midline; max is D+A=5; the frequency is 50 Hz, not 100.

Explanation

Amplitude |A|=2; F=50 Hz so T=1/50 s; D=3 is midline; max is D+A=5; the frequency is 50 Hz, not 100.

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2) Select all models that correctly represent A=5, F=4 Hz, D=−2.

S(t)=5·sin(8π·t)−2

S(t)=5·sin(2π·4·t)−2

S(t)=−5·sin(8π·t)−2

S(t)=5·sin(2π·t/4)−2

S(t)=5·sin(2π·4·t)+2

2π·4=8π, so A and B are equivalent. C flips the sign of A but keeps amplitude 5 and midline −2. D uses period incorrectly; E has wrong midline.

Explanation

2π·4=8π, so A and B are equivalent. C flips the sign of A but keeps amplitude 5 and midline −2. D uses period incorrectly; E has wrong midline.

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3) For s(t)=A·sin(2π·F·t)+D, the period T equals 1/F seconds.

True

False

Because 2πF·T=2π ⇒ T=1/F.

Explanation

Because 2πF·T=2π ⇒ T=1/F.

4) Amplitude A = 3, frequency F = 5 Hz, midline D = −2. Choose the correct model s(t).

S(t) = 3·sin(2π·5·t) + -2

S(t) = 3·sin(2π·5·t) + 2

S(t) = 3·sin(π·5·t) − 2

S(t) = 3·sin(2π·t/5) − 2

Use s(t)=A·sin(2π·F·t)+D with A=3, F=5, D=−2. πF or 1/F is incorrect in the argument.

Explanation

Use s(t)=A·sin(2π·F·t)+D with A=3, F=5, D=−2. πF or 1/F is incorrect in the argument.

5) If F is measured in Hz, then t must be measured in seconds for s(t)=A·sin(2π·F·t)+D to be dimensionally consistent.

True

False

Hz = cycles/second, so F·t is in cycles; 2π converts cycles to radians.

Explanation

Hz = cycles/second, so F·t is in cycles; 2π converts cycles to radians.

6) A wave has amplitude 0.5, frequency 60 Hz, and midline −1. Which model is correct?

S(t) = 0.5·sin(2π·t/60) − 1

S(t) = 0.5·sin(2π·60·t) − 1

S(t) = 0.5·sin(π·60·t) − 1

S(t) = 0.5·sin(60·t) − 1

Angular frequency must be 2πF, giving s(t)=0.5·sin(2π·60·t)−1.

Explanation

Angular frequency must be 2πF, giving s(t)=0.5·sin(2π·60·t)−1.

7) A wave has amplitude 2.5, period T=0.01 s, and midline 1. Write s(t). ____

T=1/F ⇒ F=100 Hz. Substitute into s(t)=A·sin(2π·F·t)+D.

Explanation

T=1/F ⇒ F=100 Hz. Substitute into s(t)=A·sin(2π·F·t)+D.

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8) For any A and D, s(t)=A·sin(2π·F·t)+D always lies between D−|A| and D+|A|.

True

False

Because −1 ≤ sin ≤ 1, the range shifts and scales accordingly.

Explanation

Because −1 ≤ sin ≤ 1, the range shifts and scales accordingly.

9) For s(t)=0.3·sin(2π·1000·t)−0.1, select all true statements.

Amplitude is 0.3

Frequency is 1000 Hz

Period is 0.001 s

Midline is y=−0.1

Maximum value is 0.2

A=0.3, F=1000 Hz ⇒ T=0.001 s, D=−0.1, max = D+A = 0.2.

Explanation

A=0.3, F=1000 Hz ⇒ T=0.001 s, D=−0.1, max = D+A = 0.2.

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12) Which changes will double the wave’s frequency for s(t)=A·sin(2π·F·t)+D? Select all that apply.

Replace F with 2F in the formula

Replace t with 2t inside the sine

Replace F with F/2 in the formula

Replace t with t/2 inside the sine

Keep A and D the same while doubling F

Doubling F or replacing t with 2t doubles the coefficient of t in the sine; keeping A and D while doubling F still doubles frequency. Using F/2 or t/2 halves frequency.

Explanation

Doubling F or replacing t with 2t doubles the coefficient of t in the sine; keeping A and D while doubling F still doubles frequency. Using F/2 or t/2 halves frequency.

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13) Which formulas are incorrect for A=4, F=3 Hz, D=1? Select all that are incorrect.

S(t)=4·sin(2π·3·t)+1

S(t)=4·sin(6π·t)+1

S(t)=4·sin(2π·t/3)+1

S(t)=4·sin(2π·3·t)+0

S(t)=4·sin(2π·3·t)−1

A and B are correct and equivalent. C uses 1/3 incorrectly; D and E have wrong midlines.

Explanation

A and B are correct and equivalent. C uses 1/3 incorrectly; D and E have wrong midlines.

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14) In s(t)=A·sin(2π·F·t)+D, the graph oscillates about the horizontal line y=D.

True

False

D is the vertical shift (midline). The output ranges from D−|A| to D+|A|.

Explanation

D is the vertical shift (midline). The output ranges from D−|A| to D+|A|.

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16) Which model has amplitude 4, frequency 25 Hz, and midline y=−3?

S(t)=4·sin(2π·25·t)−1

S(t)=4·sin(2π·25·t)−3

S(t)=−4·sin(2π·25·t)−3

S(t)=4·sin(25·t)−3

Standard form uses positive A; A=4, F=25, D=−3 ⇒ s(t)=4·sin(2π·25·t)−3. Option D lacks 2π.

Explanation

Standard form uses positive A; A=4, F=25, D=−3 ⇒ s(t)=4·sin(2π·25·t)−3. Option D lacks 2π.

17) Replacing A with −A in s(t)=A·sin(2π·F·t)+D reflects the wave across the midline without changing amplitude or frequency.

True

False

Amplitude is |A|; changing sign reflects across y=D (phase shift of π).

Explanation

Amplitude is |A|; changing sign reflects across y=D (phase shift of π).

18) A sound completes 200 cycles each second. With amplitude 1.5 and midline 2, the correct model is:

S(t)=1.5·sin(200·t)+2

S(t)=1.5·sin(π·200·t)+2

S(t)=1.5·sin(2π·200·t)+2

S(t)=1.5·sin(2π·t/200)+2

200 cycles/s ⇒ F=200 Hz. Use s(t)=A·sin(2π·F·t)+D.

Explanation

200 cycles/s ⇒ F=200 Hz. Use s(t)=A·sin(2π·F·t)+D.

19) Model a tone with amplitude 0.8, frequency 2.5 kHz, and midline 0, using Hz. ____

2.5 kHz = 2500 Hz. Insert into s(t)=A·sin(2π·F·t)+D.

Explanation

2.5 kHz = 2500 Hz. Insert into s(t)=A·sin(2π·F·t)+D.

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20) Which of the following has amplitude 6 and frequency 10 Hz with midline y=0?

S(t)=6·sin(10·t)

S(t)=6·sin(π·10·t)

S(t)=−6·sin(10·t)+0

S(t)=6·sin(2π·10·t)

Need ω=2πF=20π ⇒ s(t)=6·sin(2π·10·t).

Explanation

Need ω=2πF=20π ⇒ s(t)=6·sin(2π·10·t).