An earthquake can produce a seiche (pronounced "saysh") in a...

An earthquake can produce a seiche (pronounced "saysh") in a lake, in which the water sloshes back and forth from end to end with a remarkably large amplitude and long period. Consider a seiche produced in a rectangular farm pond, as diagrammed in the cross-sectional view of Figure P18.29 (figure not drawn to scale). Suppose that the pond is $9.15 \mathrm{~m}$ long and of uniform depth. You measure that a wave pulse produced at one end reaches the other end in $2.50 \mathrm{~s}$. (a) What is the wave speed? (b) To produce the seiche, you suggest that several people stand on the bank at one end and paddle together with snow shovels, moving them in simple harmonic motion. What must be the frequency of this motion?

Key Concepts

Simple Harmonic Motion

Simple harmonic motion (SHM) describes oscillatory motion where the restoring force on an object is proportional to its displacement from equilibrium, leading to sinusoidal oscillations. This concept is key in understanding how periodic driving forces, such as coordinated paddling, can induce oscillations in a body of water and lead to phenomena like seiches.

Wave Speed

Wave speed is defined as the distance a wave travels per unit time. It is a fundamental concept in wave mechanics and is calculated using the relation speed = distance/time. It characterizes how rapidly a disturbance propagates through a medium, which is essential for predicting wave behavior in various environments.

Standing Waves

Standing waves occur when two waves of identical frequency and amplitude travel in opposite directions and interfere, resulting in nodes (points of no movement) and antinodes (points of maximum movement). Seiches in lakes or ponds are an example of standing waves, where the water oscillates back and forth in a confined space.

Frequency

Frequency is the number of oscillations or cycles per unit time and is a crucial parameter in the study of periodic motions and waves. It determines the timing of each oscillation and, in systems exhibiting resonance, must match the natural frequency of the system to effectively amplify the oscillatory response.

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