Question

[This question contains an animated GIF image. Please refer to that image]
A designer has created an infinitely looping animation as shown in the image. It has 24 frames playing at a speed of 12 frames per second. Which of the statements is/are true?

• A. The duration of one circular loop is 3 seconds.
• B. Each dot turns white for 4 frames in each loop.
• C. If this animation is played at 8 frames per second, the speed of animation will be faster.
• D. This animation with same duration is possible with 6 frames played at 3 frames per second.

Hint:

Start from the formula duration = total frames / frames per second, and apply it once to the original animation (24 frames, 12 fps) to get a reference duration. For each statement, check whether it changes the frame count, the frame rate, or both, and compare against that same reference instead of picturing the animation playing out. Watch out for the trap in the fps-change statement: a lower frame rate always stretches the loop out, it does not speed anything up.

Answer 1

The Correct Option is B, D

To evaluate the given statements about the animation, we need to perform a few calculations and logical analysis based on the provided details:

• There are 24 frames in total.
• The animation plays at a speed of 12 frames per second.
• Let's analyze each statement:
• Statement 1: "The duration of one circular loop is 3 seconds."

The duration in seconds of the animation can be calculated using the formula: Duration (seconds) = Total frames / Frames per second = 24 / 12 = 2 seconds. Thus, this statement is false.

• Statement 2: "Each dot turns white for 4 frames in each loop."

Assuming the alternating frames repeat evenly, with a total of 24 frames, one segment of activity for turning a dot white can be: 24 frames / 6 dots = 4 frames per dot. Thus, this statement is true.

• Statement 3: "If this animation is played at 8 frames per second, the speed of animation will be faster."

If played at a lower frame rate of 8 frames per second, the time taken to complete the loop will increase: Duration = 24 / 8 = 3 seconds. Lowering the frame rate makes the animation slower, not faster. Thus, this statement is false.

• Statement 4: "This animation with the same duration is possible with 6 frames played at 3 frames per second."

With 6 frames at 3 frames per second = 6 / 3 = 2 seconds, which is equal to the original duration. Thus, this statement is true.

In summary, the true statements are:

• Each dot turns white for 4 frames in each loop.
• This animation with the same duration is possible with 6 frames played at 3 frames per second.

Answer 2

Concept:

• Frame count and frame rate are linked by $\text{duration} = \dfrac{\text{frames}}{\text{fps}}$, so two setups give the SAME duration exactly when $\dfrac{\text{frames}_1}{\text{fps}_1} = \dfrac{\text{frames}_2}{\text{fps}_2}$.
• This ratio check can be done by cross-multiplication, without ever converting to seconds -- useful for checking several statements quickly against one reference setup.
• Frame rate and loop duration are inversely related when the frame count is fixed: raising fps always shortens the loop, lowering fps always lengthens it.

Step 1: Set up the reference ratio for the original animation.
24 frames at 12 fps gives the pair $(24, 12)$.

Step 2: Test Statement 1 by cross-multiplication instead of dividing.
Statement 1 claims the loop takes 3 seconds, which is the same as claiming the pair $(3, 1)$ matches $(24, 12)$ in frames-per-second terms, i.e. 3 seconds at 1 frame per second is not what is being compared -- instead check $24 \times 1$ against $3 \times 12$: $24 \ne 36$, so the ratios do not match and the statement is false.

Step 3: Test Statement 3 using the inverse relationship, with no division at all.
The frame count stays fixed at 24. Since duration $=\dfrac{24}{\text{fps}}$, duration grows as fps falls. Dropping from 12 fps to 8 fps is a fall in fps, so the loop must take longer, not less time -- the animation plays slower, never faster. Statement 3 is false.

Step 4: Test Statement 4 by cross-multiplication against the same reference pair.
The claim is that $(6, 3)$ gives the same duration as $(24, 12)$. Cross-multiply: $6 \times 12 = 72$ and $24 \times 3 = 72$. Both sides match, so $(6, 3)$ does reproduce the same loop duration as the original, and Statement 4 is true.

Step 5: Check Statement 2 using time-per-frame instead of frames-per-dot.
Time for one frame $= \dfrac{1}{12}$ second. With the dots dividing the 24-frame loop evenly, the white phase for each dot lasts 4 frames, which is $4 \times \dfrac{1}{12} = \dfrac{1}{3}$ second -- a fixed, sensible fraction of the 2 second loop, consistent with an even split across the loop. Statement 2 is true.

Final Answer: Statements 2 and 4 are true; Statements 1 and 3 are false.