1. **Problem 1: Wave Velocity in Ocean Waves** Given: An ocean wave has a wavelength $\lambda = 20$ meters and a frequency $f = 0.5$ Hz. Unknown: Find the wave velocity $v$. Step 1: State the formula for wave velocity: $$v = f \times \lambda$$ This formula relates wave speed to frequency and wavelength. Step 2: Substitute the given values: $$v = 0.5 \times 20 = 10$$ Step 3: Interpret the result: The wave velocity is $10$ meters per second, meaning the wave crest moves across the ocean surface at this speed. --- 2. **Problem 2: Particle Acceleration in a Vibrating String** Given: A particle on a string oscillates with amplitude $A = 0.02$ m and angular frequency $\omega = 50$ rad/s. Unknown: Find the maximum particle acceleration $a_{max}$. Step 1: Use the formula for maximum acceleration in Simple Harmonic Motion (SHM): $$a_{max} = \omega^2 \times A$$ This formula calculates the peak acceleration of particles oscillating in the wave. Step 2: Substitute the values: $$a_{max} = 50^2 \times 0.02 = 2500 \times 0.02 = 50$$ Step 3: Interpret the result: The particle acceleration reaches a maximum of $50$ meters per second squared, showing how particles in the string rapidly change velocity during oscillation. --- These problems illustrate wave velocity as the speed of wave propagation and particle acceleration as the oscillatory motion of particles within the medium, both fundamental to understanding wave behavior.