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Example · Example 1

Q.A pulse travels along a stretched horizontal string, and a sound pulse travels along a column of air in a pipe. State, with a reason for each, whether the wave in the string and the wave in the air column is transverse or longitudinal.

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✓ Free question

A string can support shear stress -- a displaced element of string is pulled back toward the equilibrium line by the string's own tension acting at an angle to the displacement, so successive elements can vibrate perpendicular to the string's length while the disturbance itself runs along the length. This is exactly the condition for a transverse wave, so the pulse on the string is transverse.

Air, being a fluid, cannot support any shear stress at all -- it offers no resistance to being displaced sideways, only to being compressed or expanded (its bulk elasticity). A disturbance in air can therefore only take the form of particles moving back and forth along the very direction the disturbance travels, alternately crowding together (compression) and spreading apart (rarefaction). This is exactly the condition for a longitudinal wave, so the sound pulse in the pipe's air column is longitudinal.

✓Final answer

The string wave is transverse because the string can sustain shear (restoring) forces perpendicular to its length; the air-column wave is longitudinal because a fluid can only be compressed/rarefied along the direction of the disturbance, not sheared.

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