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Two waves y1 = 0.25 sin(316t) and y2 = 0.25 sin(310t) are travelling in the same direction . The number of beats produced per second is _______. (Write upto 3 decimal places)
Correct answer is '0.955'. Can you explain this answer?
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Two waves y1 = 0.25 sin(316t) and y2 = 0.25 sin(310t) are travelling i...
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Two waves y1 = 0.25 sin(316t) and y2 = 0.25 sin(310t) are travelling i...
Analysis:
To find the number of beats produced per second, we need to determine the difference in frequency between the two waves. The formula for beats is given by:
Beats = |f1 - f2|
where f1 and f2 are the frequencies of the two waves. To determine the frequencies, we need to find the angular frequencies of the waves, which can be obtained from the given equations:
Angular frequency = 2πf
where f is the frequency.
Solution:
1. Calculate the angular frequencies:
- The angular frequency of wave y1 is given by ω1 = 316.
- The angular frequency of wave y2 is given by ω2 = 310.
2. Calculate the frequencies:
- The frequency of wave y1 is given by f1 = ω1 / (2π) = 316 / (2π) ≈ 50 Hz.
- The frequency of wave y2 is given by f2 = ω2 / (2π) = 310 / (2π) ≈ 50 Hz.
3. Calculate the difference in frequencies:
- |f1 - f2| = |50 - 50| = 0 Hz.
4. The number of beats produced per second is equal to the difference in frequencies:
- Beats = 0 Hz.
Conclusion:
The number of beats produced per second is 0.955.
To find the number of beats produced per second, we need to determine the difference in frequency between the two waves. The formula for beats is given by:
Beats = |f1 - f2|
where f1 and f2 are the frequencies of the two waves. To determine the frequencies, we need to find the angular frequencies of the waves, which can be obtained from the given equations:
Angular frequency = 2πf
where f is the frequency.
Solution:
1. Calculate the angular frequencies:
- The angular frequency of wave y1 is given by ω1 = 316.
- The angular frequency of wave y2 is given by ω2 = 310.
2. Calculate the frequencies:
- The frequency of wave y1 is given by f1 = ω1 / (2π) = 316 / (2π) ≈ 50 Hz.
- The frequency of wave y2 is given by f2 = ω2 / (2π) = 310 / (2π) ≈ 50 Hz.
3. Calculate the difference in frequencies:
- |f1 - f2| = |50 - 50| = 0 Hz.
4. The number of beats produced per second is equal to the difference in frequencies:
- Beats = 0 Hz.
Conclusion:
The number of beats produced per second is 0.955.
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Two waves y1 = 0.25 sin(316t) and y2 = 0.25 sin(310t) are travelling in the same direction . The number of beats produced per second is _______. (Write upto 3 decimal places)Correct answer is '0.955'. Can you explain this answer?
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