Q. What is the phase difference between two particles in the same wave at a distance of half a wavelength? (2022)
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A.
0 radians
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B.
π/2 radians
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C.
π radians
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D.
3π/2 radians
Solution
The phase difference between two points separated by half a wavelength is π radians.
Correct Answer: C — π radians
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Q. What is the phase difference between two points on a wave that are 1/4 of a wavelength apart? (2021)
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A.
0 rad
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B.
π/2 rad
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C.
π rad
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D.
3π/2 rad
Solution
The phase difference Δφ is given by Δφ = (2π/λ) * Δx. For Δx = λ/4, Δφ = (2π/λ) * (λ/4) = π/2 rad.
Correct Answer: B — π/2 rad
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Q. What is the relationship between the frequency and the period of a wave? (2021)
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A.
Frequency is the square of the period
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B.
Period is the reciprocal of frequency
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C.
Frequency and period are unrelated
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D.
Period is the square root of frequency
Solution
The period T is the reciprocal of frequency f, given by T = 1/f.
Correct Answer: B — Period is the reciprocal of frequency
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Q. What is the time period of a wave with a frequency of 20 Hz? (2022)
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A.
0.05 s
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B.
0.1 s
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C.
0.2 s
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D.
0.5 s
Solution
The time period T is the reciprocal of frequency, T = 1/f. Thus, T = 1/20 Hz = 0.05 s.
Correct Answer: B — 0.1 s
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Q. What is the total mechanical energy of a simple harmonic oscillator at maximum displacement? (2022)
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A.
Zero
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B.
Maximum
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C.
Minimum
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D.
Constant
Solution
At maximum displacement, the total mechanical energy of a simple harmonic oscillator is at its maximum, as all energy is potential.
Correct Answer: B — Maximum
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Q. What is the total mechanical energy of a simple harmonic oscillator with a mass of 1 kg, amplitude of 0.1 m, and spring constant of 100 N/m? (2022)
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A.
0.5 J
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B.
1 J
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C.
2 J
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D.
4 J
Solution
The total mechanical energy E is given by E = (1/2)kA². Therefore, E = (1/2)(100)(0.1)² = 0.5 J.
Correct Answer: B — 1 J
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