Respuesta :
To find the shortest delay time for a 30-degree phase difference between two 65 Hz sine waves, follow these steps:
1. Convert frequency to period:
- The period of a wave is the inverse of its frequency. For a 65 Hz wave, the period is:
- Period = 1 / Frequency = 1 / 65 Hz ≈ 0.0153846154… s.
2. Convert seconds to milliseconds:
- Multiply the period by 1000 to convert it to milliseconds:
- Period (ms) ≈ 0.0153846154… s * 1000 = 15.3846154… ms.
3. Calculate phase difference in radians:
- 30 degrees is equivalent to π/6 radians.
4. Find the delay time:
- The delay time (Δt) in milliseconds is related to the phase difference (φ) and the period (T) by the equation:
- Δt = φ / 2πf = (π/6) / (2π * 65 Hz)
- Δt ≈ 0.00120238095… s.
5. Convert seconds to milliseconds again:
- Δt (ms) ≈ 0.00120238095… s * 1000 = 1.20238095… ms.
6. Round to the nearest hundredth:
- The shortest delay time that causes a 30-degree phase difference is approximately **1.20 milliseconds**.
Therefore, a delay of approximately 1.20 milliseconds would cause two 65 Hz sine waves to be 30 degrees out of phase.
