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Mathematical Modeling: Music and Acoustics

Description: Mathematical Modeling: Music and Acoustics
Number of Questions: 15
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Tags: mathematical modeling music acoustics
Attempted 0/15 Correct 0 Score 0

What is the mathematical equation for the frequency of a vibrating string?

  1. f = (1/2L) * sqrt(T/m)

  2. f = (1/L) * sqrt(T/m)

  3. f = (1/2L) * sqrt(m/T)

  4. f = (1/L) * sqrt(m/T)


Correct Option: A
Explanation:

The frequency of a vibrating string is given by the equation f = (1/2L) * sqrt(T/m), where L is the length of the string, T is the tension in the string, and m is the mass per unit length of the string.

What is the mathematical equation for the wavelength of a sound wave?

  1. λ = v/f

  2. λ = f/v

  3. λ = v*f

  4. λ = f*v


Correct Option: A
Explanation:

The wavelength of a sound wave is given by the equation λ = v/f, where v is the velocity of the sound wave and f is the frequency of the sound wave.

What is the mathematical equation for the intensity of a sound wave?

  1. I = P/A

  2. I = P*A

  3. I = P^2/A

  4. I = P*A^2


Correct Option: A
Explanation:

The intensity of a sound wave is given by the equation I = P/A, where P is the power of the sound wave and A is the area over which the sound wave is spread.

What is the mathematical equation for the reverberation time of a room?

  1. RT = 0.161 * V/A

  2. RT = 0.161 * A/V

  3. RT = 0.161 * V*A

  4. RT = 0.161 * A^2/V


Correct Option: A
Explanation:

The reverberation time of a room is given by the equation RT = 0.161 * V/A, where V is the volume of the room and A is the total absorption of the room.

What is the mathematical equation for the frequency of a musical note?

  1. f = 2^(n/12) * 440

  2. f = 2^(n/12) * 220

  3. f = 2^(n/12) * 880

  4. f = 2^(n/12) * 1760


Correct Option: A
Explanation:

The frequency of a musical note is given by the equation f = 2^(n/12) * 440, where n is the number of half steps above or below the note A4 (440 Hz).

What is the mathematical equation for the amplitude of a musical note?

  1. A = P/I

  2. A = I/P

  3. A = P*I

  4. A = I*P


Correct Option: A
Explanation:

The amplitude of a musical note is given by the equation A = P/I, where P is the power of the note and I is the intensity of the note.

What is the mathematical equation for the timbre of a musical note?

  1. T = f/A

  2. T = A/f

  3. T = f*A

  4. T = A*f


Correct Option: B
Explanation:

The timbre of a musical note is given by the equation T = A/f, where A is the amplitude of the note and f is the frequency of the note.

What is the mathematical equation for the loudness of a musical note?

  1. L = 20 * log(I/I_0)

  2. L = 20 * log(I_0/I)

  3. L = 20 * log(A/A_0)

  4. L = 20 * log(A_0/A)


Correct Option: A
Explanation:

The loudness of a musical note is given by the equation L = 20 * log(I/I_0), where I is the intensity of the note and I_0 is the reference intensity (10^-12 W/m^2).

What is the mathematical equation for the pitch of a musical note?

  1. P = f/A

  2. P = A/f

  3. P = f*A

  4. P = A*f


Correct Option:
Explanation:

The pitch of a musical note is given by the equation P = f, where f is the frequency of the note.

What is the mathematical equation for the duration of a musical note?

  1. D = t/A

  2. D = A/t

  3. D = t*A

  4. D = A*t


Correct Option:
Explanation:

The duration of a musical note is given by the equation D = t, where t is the time for which the note is played.

What is the mathematical equation for the attack time of a musical note?

  1. A = t/I

  2. A = I/t

  3. A = t*I

  4. A = I*t


Correct Option:
Explanation:

The attack time of a musical note is given by the equation A = t, where t is the time it takes for the note to reach its maximum amplitude.

What is the mathematical equation for the decay time of a musical note?

  1. D = t/A

  2. D = A/t

  3. D = t*A

  4. D = A*t


Correct Option:
Explanation:

The decay time of a musical note is given by the equation D = t, where t is the time it takes for the note to decay to half of its maximum amplitude.

What is the mathematical equation for the sustain time of a musical note?

  1. S = t/A

  2. S = A/t

  3. S = t*A

  4. S = A*t


Correct Option:
Explanation:

The sustain time of a musical note is given by the equation S = t, where t is the time for which the note is held at its maximum amplitude.

What is the mathematical equation for the release time of a musical note?

  1. R = t/A

  2. R = A/t

  3. R = t*A

  4. R = A*t


Correct Option:
Explanation:

The release time of a musical note is given by the equation R = t, where t is the time it takes for the note to decay to zero amplitude.

What is the mathematical equation for the envelope of a musical note?

  1. E = A(t) * D(t) * S(t) * R(t)

  2. E = A(t) + D(t) + S(t) + R(t)

  3. E = A(t) * D(t) + S(t) + R(t)

  4. E = A(t) + D(t) * S(t) + R(t)


Correct Option: A
Explanation:

The envelope of a musical note is given by the equation E = A(t) * D(t) * S(t) * R(t), where A(t) is the attack function, D(t) is the decay function, S(t) is the sustain function, and R(t) is the release function.

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