5. A piano tuner strikes a tuning fork for the note middle C and creates a sound wave. The tuning fork makes 252 vibrations every second. If the amplitude of this wave is 2 units, model the wave with a function of the form y = A · sin(Bt).
5. A piano tuner strikes a tuning fork for the note middle C and creates a sound wave. The tuning fork makes 252 vibrations every second. If the amplitude of this wave is 2 units, model the wave with a function of the form y = A · sin(Bt).
5. A piano tuner strikes a tuning fork for the note middle C and creates a sound wave. The tuning fork makes 252 vibrations every second. If the amplitude of this wave is 2 units, model the wave with a function of the form y = A · sin(Bt).
Sinusoidal modeling: use your knowledge of amplitude, period, vertical translations, and horizontal translations along with your higher order of thinking skills to find functions that model the following.
Transcribed Image Text:**Problem 5: Sound Wave Modeling**
A piano tuner strikes a tuning fork for the note middle C and creates a sound wave. The tuning fork makes 252 vibrations every second. If the amplitude of this wave is 2 units, model the wave with a function of the form \( y = A \cdot \sin(Bt) \).
**Explanation:**
- **Sound Wave Frequency:** The tuning fork vibrates 252 times per second, indicating the frequency.
- **Amplitude:** The wave's amplitude is given as 2 units.
To model the sound wave:
- Let \( A = 2 \) because the amplitude is 2.
- The frequency \( f = 252 \) vibrations per second implies \( B = 2\pi f = 2\pi \times 252 \).
The wave function is represented as \( y = 2 \cdot \sin(504\pi t) \).
This function describes the displacement of the wave at any time \( t \).
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
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