Oscillations & Waves
Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). If A = 2 m, k = 3 rad/m, and ω = 6 rad/s, what is the amplitude of the wave?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
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Solution
The amplitude of the wave is given directly by A in the wave equation. Here, A = 2 m.
Correct Answer: B — 2 m
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Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'A' represent?
A.
Wavelength
B.
Amplitude
C.
Frequency
D.
Speed
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Solution
'A' represents the amplitude of the wave, which is the maximum displacement from the equilibrium position.
Correct Answer: B — Amplitude
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Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does 'k' represent?
A.
Amplitude
B.
Wave number
C.
Frequency
D.
Angular frequency
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Solution
'k' is the wave number, which is related to the wavelength λ by the equation k = 2π/λ.
Correct Answer: B — Wave number
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Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What is the phase velocity of the wave?
A.
A/k
B.
ω/k
C.
k/ω
D.
Aω
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Solution
The phase velocity v is given by v = ω/k.
Correct Answer: B — ω/k
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Q. A wave travels along a string with a speed of 300 m/s and has a frequency of 150 Hz. What is the wavelength of the wave?
A.
1.0 m
B.
2.0 m
C.
3.0 m
D.
4.0 m
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Solution
Wavelength λ is given by λ = v/f. Here, v = 300 m/s and f = 150 Hz. Thus, λ = 300/150 = 2.0 m.
Correct Answer: B — 2.0 m
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Q. A wave travels at a speed of 300 m/s and has a frequency of 150 Hz. What is its wavelength?
A.
2 m
B.
1.5 m
C.
3 m
D.
0.5 m
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Solution
The wavelength λ can be calculated using the formula v = fλ. Thus, λ = v/f = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 1.5 m
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Q. A wave travels through a medium with a frequency of 500 Hz and a wavelength of 2 m. What is the speed of the wave?
A.
1000 m/s
B.
250 m/s
C.
500 m/s
D.
2000 m/s
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Solution
The speed of a wave is given by the formula v = fλ, where f is the frequency and λ is the wavelength. Here, v = 500 Hz * 2 m = 1000 m/s.
Correct Answer: A — 1000 m/s
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Q. A wave travels through a medium with a speed of 300 m/s and has a frequency of 150 Hz. What is the wavelength?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
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Solution
Wavelength λ = v/f = 300/150 = 2 m.
Correct Answer: B — 2 m
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Q. A wave travels through a medium with a speed of 300 m/s and has a frequency of 150 Hz. What is the wavelength of the wave?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
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Solution
The wavelength λ can be calculated using the formula v = fλ. Thus, λ = v/f = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 2 m
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Q. A wave travels through a medium with a speed of 300 m/s and has a frequency of 150 Hz. What is its wavelength?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
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Solution
Wavelength (λ) can be calculated using the formula λ = v/f. Here, λ = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 2 m
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Q. A wave travels with a frequency of 500 Hz and a wavelength of 2 m. What is its speed?
A.
250 m/s
B.
1000 m/s
C.
500 m/s
D.
200 m/s
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Solution
The speed of the wave is given by v = fλ. Here, v = 500 Hz * 2 m = 1000 m/s.
Correct Answer: A — 250 m/s
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Q. A wave travels with a speed of 300 m/s and has a frequency of 150 Hz. What is its wavelength?
A.
1 m
B.
2 m
C.
3 m
D.
4 m
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Solution
Wavelength (λ) can be calculated using the formula λ = v/f. Here, λ = 300 m/s / 150 Hz = 2 m.
Correct Answer: B — 2 m
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Q. For a damped oscillator, what is the relationship between the natural frequency and the damped frequency?
A.
Damped frequency is greater
B.
Damped frequency is equal
C.
Damped frequency is less
D.
No relationship
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Solution
The damped frequency is less than the natural frequency due to the effect of damping.
Correct Answer: C — Damped frequency is less
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Q. If a damped oscillator has a damping ratio of 0.5, what type of damping does it exhibit?
A.
Underdamped
B.
Critically damped
C.
Overdamped
D.
None of the above
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Solution
A damping ratio (ζ) < 1 indicates underdamped motion.
Correct Answer: A — Underdamped
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Q. If a damped oscillator has a mass of 5 kg, a spring constant of 20 N/m, and a damping coefficient of 1 kg/s, what is the natural frequency of the system?
A.
1 Hz
B.
2 Hz
C.
3 Hz
D.
4 Hz
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Solution
Natural frequency (ω_n) = √(k/m) = √(20/5) = √4 = 2 Hz.
Correct Answer: B — 2 Hz
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Q. If a forced oscillator is driven at a frequency much lower than its natural frequency, what happens to the amplitude?
A.
Increases significantly
B.
Decreases
C.
Remains constant
D.
Fluctuates
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Solution
At frequencies much lower than the natural frequency, the amplitude of the forced oscillator increases significantly.
Correct Answer: B — Decreases
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Q. If a simple harmonic oscillator has a frequency of 1 Hz, what is the time period?
A.
0.5 s
B.
1 s
C.
2 s
D.
4 s
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Solution
Time period (T) is the reciprocal of frequency (f). T = 1/f = 1/1 = 1 s.
Correct Answer: B — 1 s
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Q. If a simple harmonic oscillator has a maximum displacement of 5 cm, what is the amplitude?
A.
2.5 cm
B.
5 cm
C.
10 cm
D.
0 cm
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Solution
The amplitude of a simple harmonic oscillator is defined as the maximum displacement from the equilibrium position, which is 5 cm in this case.
Correct Answer: B — 5 cm
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Q. If a simple harmonic oscillator has a total energy E, what is the kinetic energy when the displacement is half of the amplitude?
A.
E/4
B.
E/2
C.
3E/4
D.
E
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Solution
The total energy E is conserved. When the displacement is half the amplitude, the potential energy is (1/2)E, so the kinetic energy is E - (1/2)E = (1/2)E.
Correct Answer: C — 3E/4
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Q. If a sound wave has a frequency of 440 Hz, what is its period?
A.
0.00227 s
B.
0.0045 s
C.
0.01 s
D.
0.1 s
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Solution
The period (T) is the inverse of frequency (f); T = 1/f = 1/440 ≈ 0.00227 s.
Correct Answer: A — 0.00227 s
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Q. If the amplitude of a damped oscillator decreases to half its value in 5 seconds, what is the damping ratio?
A.
0.1
B.
0.2
C.
0.3
D.
0.4
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Solution
Using the formula A(t) = A_0 e^(-ζω_nt), we find ζ = 0.2.
Correct Answer: B — 0.2
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Q. If the amplitude of a simple harmonic motion is doubled, how does the maximum velocity change?
A.
It doubles
B.
It quadruples
C.
It remains the same
D.
It halves
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Solution
Maximum velocity V_max = Aω. If A is doubled, V_max also doubles.
Correct Answer: A — It doubles
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Q. If the amplitude of a simple harmonic motion is doubled, how does the total energy change?
A.
Remains the same
B.
Doubles
C.
Quadruples
D.
Halves
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Solution
The total energy E in SHM is given by E = (1/2)kA². If A is doubled, E becomes (1/2)k(2A)² = 4(1/2)kA², which is quadrupled.
Correct Answer: C — Quadruples
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Q. If the amplitude of a simple harmonic motion is halved, how does the maximum velocity change?
A.
Halved
B.
Doubled
C.
Remains the same
D.
Quadrupled
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Solution
Maximum velocity V_max = ωA. If A is halved, V_max is also halved.
Correct Answer: A — Halved
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Q. If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?
A.
Remains the same
B.
Doubles
C.
Quadruples
D.
Halves
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Solution
The total energy in simple harmonic motion is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 2^2 = 4.
Correct Answer: C — Quadruples
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Q. If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?
A.
It remains the same
B.
It doubles
C.
It quadruples
D.
It halves
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Solution
The total energy of a simple harmonic oscillator is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.
Correct Answer: C — It quadruples
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Q. If the amplitude of a simple harmonic oscillator is halved, how does the total energy change?
A.
Remains the same
B.
Halved
C.
Doubled
D.
Quadrupled
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Solution
The total energy in SHM is proportional to the square of the amplitude. If amplitude is halved, energy is reduced to (1/2)^2 = 1/4, which is halved.
Correct Answer: B — Halved
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Q. If the amplitude of a wave is doubled, how does the energy of the wave change?
A.
Remains the same
B.
Doubles
C.
Increases by a factor of four
D.
Increases by a factor of eight
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Solution
The energy of a wave is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.
Correct Answer: C — Increases by a factor of four
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Q. If the amplitude of a wave is doubled, what happens to its energy?
A.
Remains the same
B.
Doubles
C.
Increases by a factor of four
D.
Increases by a factor of eight
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Solution
The energy of a wave is proportional to the square of its amplitude. Therefore, if the amplitude is doubled, the energy increases by a factor of four.
Correct Answer: C — Increases by a factor of four
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Q. If the amplitude of a wave is tripled, how does the energy of the wave change?
A.
Increases by a factor of 3
B.
Increases by a factor of 6
C.
Increases by a factor of 9
D.
Remains the same
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Solution
Energy is proportional to the square of the amplitude, so if amplitude is tripled, energy increases by a factor of 3^2 = 9.
Correct Answer: C — Increases by a factor of 9
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