During a lab, a student tapes a ruler to a lab table and sets the ruler in motion. A laser detector pointed at the ruler records how many times the ruler vibrates back and forth in a period of time.

Question

A 3 column table with 4 rows. The first column is labeled trial with entries 1, 2, 3, 4. The second column is labeled number of cycles with entries 10, 11, 13, 12. The last column is labeled time in seconds with entries .25, .30, .31, .33.
What is the order of trials from least to greatest pitch?

One; Two; Three; Four
One; Two; Four; Three
Three; One; Two; Four
Four; Two; One; Three

Answer 1

To determine the order of trials from least to greatest pitch, we need to find the frequency (pitch) for each trial, which can be calculated using the formula:

\[ \text{Frequency} = \frac{\text{Number of Cycles}}{\text{Time in seconds}} \]

Now let's calculate the frequencies for each trial:

1. Trial 1:

   • Number of Cycles = 10
   • Time = 0.25 seconds
   • Frequency = \( \frac{10}{0.25} = 40 , \text{Hz} \)

2. Trial 2:

   • Number of Cycles = 11
   • Time = 0.30 seconds
   • Frequency = \( \frac{11}{0.30} \approx 36.67 , \text{Hz} \)

3. Trial 3:

   • Number of Cycles = 13
   • Time = 0.31 seconds
   • Frequency = \( \frac{13}{0.31} \approx 41.94 , \text{Hz} \)

4. Trial 4:

   • Number of Cycles = 12
   • Time = 0.33 seconds
   • Frequency = \( \frac{12}{0.33} \approx 36.36 , \text{Hz} \)

Now we can summarize the frequencies:

• Trial 1: 40 Hz
• Trial 2: 36.67 Hz
• Trial 3: 41.94 Hz
• Trial 4: 36.36 Hz

Next, let's order these frequencies from least to greatest:

1. Trial 4: 36.36 Hz
2. Trial 2: 36.67 Hz
3. Trial 1: 40 Hz
4. Trial 3: 41.94 Hz

Thus, the order from least to greatest pitch (circle of trials) is:

Four; Two; One; Three

The correct answer is: Four; Two; One; Three.