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Waves - Case Studies - help4

The wavelength of a wave is the length of the repeating unit within the wave pattern. It is typically measured as the distance between two adjacent crests. The amplitude of a wave refers to the maximum distance that a particle on the medium is displaced from its rest position as the wave passes through it. It is often measured as the vertical distance from the resting position to the crest.

There are three similar versions of this question. Here is one of the versions:

Version 1:

The diagram at the right is a snapshot in time of a wave moving along a rope. Which diagram below represents a wave moving through the same rope but having one-half the wavelength and twice the amplitude? Tap on an image to select or deselect it.

You have to make two decisions to be successful with this question. You have to make a Wavelength decision and you have to make an Amplitude decision.

Wavelength Decision
You can use the background grid to determine the wavelength of the wave. You can count the squares. It can be thought of as the distance between one crest and the next adjacent crest. Once you determine the wavelength in the given diagram, look for an answer option that shows one-half that value for wavelength. You can do the square counting again to be sure. But in the end, you are looking for less stretched out wave; the repeating unit will repeat from often over the length of the diagram.

Amplitude Decision
You can use the background grid to determine the amplitude of the wave. You can count the squares. It can be thought of as the vertical distance from the resting position (the mid-line on the diagram) to the crest. Once you determine the amplitude in the given diagram, look for an answer option that shows twice that value for amplitude. You can count squares again to be sure. But in the end, you are looking for a taller wave.

These two decisions should allow you to narrow the answer options down to one.

Try these links to The Physics Classroom Tutorial for more help with understanding wave properties:

The Anatomy of a Wave (wavelength and amplitude)