Question

snapshots of four periodic waves are modeled below. each wave is modeled on the same grid. rank the waves from shortest wavelength to longest wavelength. shortest wavelength longest wavelength

Explanation:

Step1: Understand Wavelength

Wavelength is the distance between two consecutive identical points (like peaks or troughs) on a wave. On a grid, we can count the number of cycles (or the grid units per cycle) to compare wavelengths. Fewer grid units per cycle mean a shorter wavelength; more grid units per cycle mean a longer wavelength.

Step2: Analyze Each Wave

• Third Wave (the one with the most cycles): It has the most number of cycles in the same grid length, so its wavelength is the shortest.
• First Wave: Has more cycles than the second and fourth but fewer than the third.
• Fourth Wave: Has fewer cycles than the first and third, more than the second? Wait, no, let's count cycles. Let's assume the grid has columns. Let's say each wave spans the same horizontal grid length (same number of columns).
• Third wave: Let's say 8 cycles.
• First wave: 5 cycles.
• Fourth wave: 4 cycles.
• Second wave: 3 cycles. Wait, no, the second wave (the one with the larger peaks) has 3 cycles? Wait, looking at the images:
• Top (first): 5 small cycles.
• Second (middle top): 3 large cycles.
• Third (middle bottom): 8 very small cycles.
• Fourth (bottom): 4 medium cycles.

So the number of cycles from most to least: Third (8) > First (5) > Fourth (4) > Second (3). Since more cycles mean shorter wavelength (because wavelength = distance / number of cycles; same distance, more cycles → smaller wavelength), so the order from shortest to longest is Third, First, Fourth, Second.

Answer:

Shortest wavelength: Third wave (the one with the most dense cycles)
Then: First wave (5 cycles)
Then: Fourth wave (4 cycles)
Longest wavelength: Second wave (3 cycles)

So the ranking from shortest to longest is: Third wave, First wave, Fourth wave, Second wave.