Tuning Fork 440Hz Quiz: Tuning Fork 440Hz Period And Model

1) For a pure sine wave, the period equals the time between consecutive peaks.

True

False

Consecutive peaks are exactly one cycle apart for a sine wave, so the time between peaks equals T.

Explanation

Consecutive peaks are exactly one cycle apart for a sine wave, so the time between peaks equals T.

2) A tuning fork vibrates at 440 Hz. What is its period T in seconds?

1/440

0.004545

0.002273

1/220

Frequency F=440 cycles per second. Period T=1/F=1/440 s ≈ 0.002273 s.

Explanation

Frequency F=440 cycles per second. Period T=1/F=1/440 s ≈ 0.002273 s.

3) For s(t)=1.5·sin(2π·440·t)+0, select all true statements.

The period is 1/440 s

The angular frequency is 2π·440 rad/s

The maximum value is 1.5

The midline is y=0

The frequency is 440 cycles per second

Amplitude is 1.5 so max is 1.5. F=440 Hz so T=1/440 s and ω=2πF=2π·440. Midline D=0.

Explanation

Amplitude is 1.5 so max is 1.5. F=440 Hz so T=1/440 s and ω=2πF=2π·440. Midline D=0.

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4) If the frequency doubles, the period halves.

True

False

T=1/F. Replacing F with 2F gives T_new=1/(2F)=T/2.

Explanation

T=1/F. Replacing F with 2F gives T_new=1/(2F)=T/2.

5) Which actions halve the period T for s(t)=A·sin(2π·F·t)+D? Select all that apply.

Replace F with 2F

Replace t with 2t inside the sine

Replace F with F/2

Replace t with t/2 inside the sine

Keep A and D the same while doubling F

Period T=1/F. Doubling F halves T. Replacing t with 2t makes the argument 2× larger, doubling frequency and halving period. Keeping A and D while doubling F also halves period. Using F/2 or t/2 doubles T.

Explanation

Period T=1/F. Doubling F halves T. Replacing t with 2t makes the argument 2× larger, doubling frequency and halving period. Keeping A and D while doubling F also halves period. Using F/2 or t/2 doubles T.

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6) Changing amplitude A or midline D does not change frequency or period.

True

False

F and T depend only on the coefficient of t inside the sine, not on A or D.

Explanation

F and T depend only on the coefficient of t inside the sine, not on A or D.

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8) Compute the period of a 440 Hz wave. Choose the decimal to 6 significant digits.

11/14

T=1/440 ≈ 0.002272727… which rounds to 0.00227305 to 6 significant digits.

Explanation

T=1/440 ≈ 0.002272727… which rounds to 0.00227305 to 6 significant digits.

9) Which has the shorter period?

A 440 Hz tone

A 220 Hz tone

Both have the same period

Cannot be determined

Higher frequency means shorter period. T_440=1/440

Explanation

Higher frequency means shorter period. T_440=1/440

10) A tone has amplitude 1 and frequency 0.44 kHz. Choose the correct model.

S(t)=1·sin(2π·0.44·t)

S(t)=1·sin(2π·440·t)

S(t)=1·sin(440·t)

S(t)=1·sin(2π·t/0.44)

0.44 kHz = 440 Hz. Use s(t)=A·sin(2π·F·t)+D with A=1, F=440, D=0.

Explanation

0.44 kHz = 440 Hz. Use s(t)=A·sin(2π·F·t)+D with A=1, F=440, D=0.

11) Choose a correct displacement with amplitude 0.6, frequency 440 Hz, midline −0.2, and initial phase π/2.

S(t) = 0.6·sin(2π·440·t + 1.570796) + -0.2

S(t) = 0.6·sin(2π·440·t + 3.141593) + -0.2

S(t) = 0.6·sin(2π·440·t + 1.570796) + 0.2

S(t)=0.6·sin(2π·t/440 + π/2) − 0.2

Use s(t)=A·sin(2π·F·t+φ)+D with F=440. Options C and D have wrong midline or wrong frequency term.

Explanation

Use s(t)=A·sin(2π·F·t+φ)+D with F=440. Options C and D have wrong midline or wrong frequency term.

12) Which statements are incorrect for a 440 Hz sine model s(t)=A·sin(2π·440·t)+D? Select all that are incorrect.

Its period is 0.002273 s (approx)

Its angular frequency is 880π rad/s

Its period is 1/220 s

Replacing 440 with 880 doubles the frequency

Replacing 440 with 110 halves the frequency

A is correct. B is correct since ω=2π·440=880π. C is incorrect because 1/220 is twice the true period. D and E describe valid frequency scalings.

Explanation

A is correct. B is correct since ω=2π·440=880π. C is incorrect because 1/220 is twice the true period. D and E describe valid frequency scalings.

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14) For any periodic sine model s(t)=A·sin(2π·F·t)+D, the period equals T=1/F.

True

False

One full cycle requires 2π·F·T=2π. Solving gives T=1/F.

Explanation

One full cycle requires 2π·F·T=2π. Solving gives T=1/F.

15) Write the displacement function for a 440 Hz tone with amplitude 0.8 about midline 0. Use s(t)=A·sin(2π·F·t)+D. ____

Substitute A=0.8, F=440, D=0 into s(t)=A·sin(2π·F·t)+D.

Explanation

Substitute A=0.8, F=440, D=0 into s(t)=A·sin(2π·F·t)+D.

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16) Select all models that correctly represent amplitude 2, frequency 440 Hz, midline 0.

S(t)=2·sin(2π·440·t) + 0

S(t)=−2·sin(2π·440·t) + 0

S(t)=2·sin(880π·t)

S(t)=2·sin(2π·t/440)

S(t)=2·sin(2π·440·t)+1

2π·440=880π. A negative amplitude flips phase but keeps amplitude 2 and midline 0. Option D uses 1/F inside the sine which is incorrect for frequency. Option E changes the midline.

Explanation

2π·440=880π. A negative amplitude flips phase but keeps amplitude 2 and midline 0. Option D uses 1/F inside the sine which is incorrect for frequency. Option E changes the midline.

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18) If F is in Hz then t must be in seconds to keep 2π·F·t dimensionless.

True

False

Hz is 1/second. F·t is cycles. Multiplying by 2π yields radians, which are dimensionless.

Explanation

Hz is 1/second. F·t is cycles. Multiplying by 2π yields radians, which are dimensionless.

19) Compute the period of a 440 Hz tuning fork to 6 decimal places. ____ s

T=1/440 ≈ 0.002272727… Rounded to 6 decimal places gives 0.002273 s.

Explanation

T=1/440 ≈ 0.002272727… Rounded to 6 decimal places gives 0.002273 s.

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20) Select all correct 440 Hz displacement models with amplitude 1 and midline 0.

S(t)=sin(2π·440·t)

S(t)=sin(880π·t)

S(t)=sin(2π·t/440)

S(t)=−sin(2π·440·t)

S(t)=sin(2π·440·t)+1

A and B are equivalent since 2π·440=880π. D flips phase but amplitude remains 1 and midline is 0. Option C uses 1/F, which is incorrect here. Option E shifts the midline.

Explanation

A and B are equivalent since 2π·440=880π. D flips phase but amplitude remains 1 and midline is 0. Option C uses 1/F, which is incorrect here. Option E shifts the midline.

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Tuning Fork 440Hz Quiz: Tuning Fork 440Hz Period and Model