physics : class11 Sinusoidal Function : Periodic Functions : Oscillations and Waves MCQ Questions and Answers
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Sinusoidal Function
MCQ questions and answers.
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MCQ Questions
1. What is the amplitude of the sinusoidal function y = 5 sin x?
A.
1
B.
5
C.
π
D.
10
Correct Answer:
5
Explanation:
For a function y = A sin x, the amplitude is the absolute value of A. Therefore, the amplitude is 5.
2. What is the maximum value of y = 3 sin x?
A.
0
B.
1
C.
3
D.
-3
Correct Answer:
3
Explanation:
Since the sine function ranges from -1 to 1, multiplying it by 3 gives a maximum value of 3.
3. What is the minimum value of y = 4 cos x?
A.
-4
B.
-1
C.
0
D.
4
Correct Answer:
-4
Explanation:
The cosine function has a minimum value of -1. Thus, the minimum value of 4 cos x is 4 × (-1) = -4.
4. What is the period of the sinusoidal function y = sin x?
A.
π/2
B.
π
C.
2π
D.
4π
Correct Answer:
2π
Explanation:
The basic sine function repeats its values after an increase of 2π in its argument, so its period is 2π.
5. What is the period of y = sin 2x?
A.
4π
B.
2π
C.
π
D.
π/2
Correct Answer:
π
Explanation:
For y = sin bx, the period is 2π divided by |b|. Here b = 2, so the period is 2π/2 = π.
6. What is the value of sin(π/2)?
A.
-1
B.
0
C.
1/2
D.
1
Correct Answer:
1
Explanation:
On the unit circle, the sine of π/2 radians is 1.
7. Which function has an amplitude of 2?
A.
y = sin x
B.
y = 2 sin x
C.
y = (1/2) sin x
D.
y = sin 2x
Correct Answer:
y = 2 sin x
Explanation:
In y = A sin x, the amplitude is |A|. Only y = 2 sin x has amplitude 2.
8. In the sinusoidal function y = sin(x + π/2), the graph of y = sin x is shifted in which direction?
A.
π/2 to the right
B.
π/2 to the left
C.
π to the right
D.
π to the left
Correct Answer:
π/2 to the left
Explanation:
In sin(x + φ), a positive phase inside the bracket shifts the graph horizontally to the left by φ. Therefore, the shift is π/2 to the left.
9. What is the frequency of a sinusoidal function whose period is 2 seconds?
A.
0.25 Hz
B.
0.5 Hz
C.
2 Hz
D.
4 Hz
Correct Answer:
0.5 Hz
Explanation:
Frequency and period are related by f = 1/T. For T = 2 seconds, f = 1/2 = 0.5 Hz.
10. For y = 6 sin(3x), which quantity determines the amplitude?
A.
The number 3
B.
The variable x
C.
The number 6
D.
The sine function
Correct Answer:
The number 6
Explanation:
The coefficient multiplying the sine function determines the amplitude. Therefore, the amplitude of y = 6 sin(3x) is determined by 6.
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