Amplitude and Period

Show your work for each problem.

1.
What is the amplitude of ?
1. a)
2. b)
3. c)
4. d)
Answer:
In , the coefficient . The amplitude is .
2.
What is the period of ?
1. a)
2. b)
3. c)
4. d)
Answer:
With , the period is .
3.
What is the amplitude of ?
Answer: 4
The coefficient . The amplitude is . The negative sign causes a reflection, not a negative amplitude.
4.
What is the period of ? (Answer in terms of , e.g., type '2pi')
Answer: 2pi
For , we have . Period . This is the standard period of cosine.
5.
For , what is the amplitude?
1. a)
2. b)
3. c)
4. d)
Answer:
In , the coefficient (in front of sine). The amplitude is . The 4 affects the period, not the amplitude.
6.
Find the amplitude and period of .
Answer: Amplitude = 3, Period = pi
1. What is the value of (coefficient in front of cosine)? 3
2. What is the amplitude? (Remember: amplitude = ) 3
3. What is the value of (coefficient of inside cosine)? 2
4. Calculate the period using . (Answer in terms of pi) pi
7.
What is the period of ? (Answer in terms of , e.g., '4pi')
Answer: 4pi
Here . Period .
8.
Which function has amplitude 4 and period ?
1. a)
2. b)
3. c)
4. d)
Answer:
has (amplitude = 4) and (period = ).
9.
Find the amplitude and period of .
Answer: Amplitude = 1/2, Period = pi/2
1. What is the value of ? 1/2
2. What is the amplitude? 1/2
3. What is the value of ? 4
4. What is the period? (Use pi/2 format) pi/2
10.
A wave oscillates between and . What is the amplitude?
1. a)
2. b)
3. c)
4. d)
Answer:
Amplitude = . The wave reaches 6 units above and below its midline ().
11.
If the frequency of a wave is , what is the value of ?
Answer: 3
Frequency = , so . Therefore , so .
12.
Write the equation of a sine wave with amplitude 3 and period .
Answer: y = 3sin(x/2)
1. For amplitude 3, what should be? 3
2. Use the period formula: . Solve for . 1/2
3. Write the equation with your values. y = 3sin(x/2)
13.
A sound wave has frequency 440 Hz. What is the period in seconds? (Round to 4 decimal places)
Answer: 0.0023
Period = seconds, or about 2.27 milliseconds. This is the note A4.
14.
A cosine wave has max value 7 and min value 1. Find the amplitude and midline.
Answer: Amplitude = 3, Midline = 4
1. Calculate amplitude using . 3
2. Calculate the midline using . 4
3. If this is , what is (vertical shift)? 4
15.
European AC power is 230V at 50 Hz. What is the equation for voltage if is in seconds?
1. a)
2. b)
3. c)
4. d)
Answer:
The 230V is RMS voltage; peak voltage (amplitude) = V. For 50 Hz, . So .
16.
Write the equation for a cosine wave with amplitude 2, period , reflected across the x-axis.
Answer: y = -2cos(4x)
1. For amplitude 2, what is ? 2
2. For reflection across x-axis, should be positive or negative? negative
3. What value of gives amplitude 2 with reflection? -2
4. From period , solve for . 4
5. Write the final equation. y = -2cos(4x)