Question

amir observes wave 1 and wave 2 crashing into each other at two different intervals. his experiments produce wave 3 and wave 4. amir records his data in a table. amir’s waves

wave	information
2	amplitude of 4 cm
3	amplitude of 7 cm
4	amplitude of 3 cm

what is the best statement about the data collected in amir’s table?
○ wave 3 resulted from destructive interference, and wave 4 resulted from constructive interference.
○ waves 3 and 4 resulted from constructive interference.
○ waves 3 and 4 resulted from destructive interference.
○ wave 3 resulted from constructive interference, and wave 4 resulted from destructive interference.

Explanation:

To solve this, we analyze wave interference:

Step 1: Recall Interference Types

• Constructive Interference: When two waves overlap, the resulting wave’s amplitude is the sum of the original amplitudes (total amplitude increases).
• Destructive Interference: When two waves overlap, the resulting wave’s amplitude is the absolute difference of the original amplitudes (total amplitude decreases).

Step 2: Analyze Wave 3

Waves 1 (amplitude = 6 cm) and 2 (amplitude = 4 cm) combine to make Wave 3 (amplitude = 7 cm).

• Sum of amplitudes: \( 6 + 4 = 10 \) cm (not 7).
• Difference of amplitudes: \( |6 - 4| = 2 \) cm (not 7). Wait, no—wait, maybe the waves are not perfectly in-phase or out-of-phase, but the key is:
• If the resulting amplitude is between the sum and difference, but here:

Wait, no—wait, constructive interference is when amplitudes add (so result > either original), destructive is when they subtract (result < at least one original).

Wave 3 (7 cm) is greater than Wave 2 (4 cm) but less than Wave 1 (6 cm)? No, 7 > 6. Wait, 6 + 4 = 10 (sum), but 7 is less than 10, but greater than both 6 and 4. Wait, maybe the problem is simplified:

• Constructive: result is sum (or close, but here, 6 + 4 = 10, but Wave 3 is 7—no, maybe I misread. Wait, no—wait, the table: Wave 1: 6 cm, Wave 2: 4 cm, Wave 3: 7 cm, Wave 4: 3 cm.

Wait, let’s recalculate:

• For Wave 3: If constructive, amplitude should be \( 6 + 4 = 10 \)? No, that’s not matching. Wait, maybe the waves are not both positive? No, amplitude is positive. Wait, maybe the problem is using a simplified approach:
• Constructive interference: resulting amplitude is greater than at least one original wave.
• Destructive interference: resulting amplitude is less than at least one original wave.

Wave 3: 7 cm. Original waves: 6 cm and 4 cm. 7 > 6 (so greater than one original) → constructive (since it’s a combination that increases amplitude relative to one wave).

Wave 4: 3 cm. Original waves: 6 cm and 4 cm. 3 < 4 (so less than one original) → destructive (since it’s a combination that decreases amplitude relative to one wave).

Step 3: Evaluate the Options

• Option 1: “Wave 3 (destructive), Wave 4 (constructive)”—Incorrect (Wave 3 is constructive, Wave 4 is destructive).
• Option 2: “Both constructive”—Incorrect (Wave 4 is 3, less than 4, so destructive).
• Option 3: “Both destructive”—Incorrect (Wave 3 is 7, greater than 6, so constructive).
• Option 4: “Wave 3 (constructive), Wave 4 (destructive)”—Matches our analysis.

Answer:

Wave 3 resulted from constructive interference, and Wave 4 resulted from destructive interference. (The corresponding option, e.g., the last option in the list.)