A fisherman notices that his boat is moving up and down...

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes $2.5 \mathrm{~s}$ for the boat to travel from its highest point to its lowest, a total distance of $0.53 \mathrm{~m} .$ The fisherman sees that the wave crests are spaced $4.8 \mathrm{~m}$ apart. (a) How fast are the waves traveling? (b) What is the amplitude of each wave? (c) If the total vertical distance traveled by the boat were $0.30 \mathrm{~m}$ but the other data remained the same, how would the answers to parts (a) and (b) change?

Key Concepts

Amplitude

Amplitude is the maximum displacement of a point on a wave from its equilibrium position. It reflects the energy or intensity of the wave, and in oscillatory contexts, it is often half of the total vertical distance traveled from the highest to the lowest point.

Period

The period is the time taken for one complete cycle of a periodic motion. In many practical situations, such as oscillatory movements influenced by waves, the period is used to relate time measurements to other wave properties like frequency and wave speed.

Wave Speed

Wave speed is the rate at which a wave propagates through a medium. It is determined by the distance between successive points that are in phase (wavelength) and the period of the wave. In many contexts, such as water waves, knowing the speed is crucial for predicting how a disturbance will move over time.

Wavelength

Wavelength refers to the spatial period of a wave—the distance between successive crests, troughs, or other corresponding points in the cycle of a periodic signal. It is a fundamental property in understanding the spatial characteristics of waves.

Simple Harmonic Motion

Simple harmonic motion is a type of oscillatory motion where the restoring force is directly proportional to the displacement from an equilibrium position, resulting in sinusoidal oscillations. It is a key concept in analyzing phenomena like waves, pendulums, and other periodic motions.

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