Question

The sound wave of two music notes can be represented by the function y = 2sin2x and y = −sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?

x = 0°, 30°, 90°, 150°
x = 0°, 90°, 210°, 330°
x = 30°, 150°, 180°, 270°
x = 180°, 210°, 270°, 330°

Answer 1

Based on the general form of a wave function, the times the frequencies of the sound waves be the same in the interval [0°, 360°) is x = 180°, 210°, 270°, 330°.

What is the frequency and Period of a wave?

Frequency is the number of vibrations of a wave per second.

The period of a wave is the time taken for one complete vibration.

Frequency and Period are inversely related.

• Frequency = 1/Period

Using the general form of a wave function:

• Asin(bx-c)+d

where;

• A = amplitude
• period = 2π/b
• c = phase shift
• d = vertical shift

From the two wave functions:

y = 2sin2x

b = 2

period = 2π/2

period = π = 180°

Frequency =

y = −sin x

b = 1

Period = 2π/1

Period = 2π = 360°

Therefore, the times the frequencies of the sound waves be the same in the interval [0°, 360°) is x = 180°, 210°, 270°, 330°.

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