1. **Problem 1: Wave Velocity in Ocean Waves** Given: An ocean wave has a wavelength $\lambda = 20$ m 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: $$v = 0.5 \times 20 = 10 \text{ m/s}$$ Step 3: Interpretation: The wave velocity $v = 10$ m/s means the wave crest moves across the ocean surface at 10 meters per second. --- 2. **Problem 2: Particle Acceleration in a String Wave** Given: A particle in a string wave 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 SHM: $$a_{max} = \omega^2 A$$ This formula comes from the fact that particle acceleration in SHM is proportional to displacement and angular frequency squared. Step 2: Substitute the values: $$a_{max} = 50^2 \times 0.02 = 2500 \times 0.02 = 50 \text{ m/s}^2$$ Step 3: Interpretation: The particle acceleration reaches a maximum of 50 m/s$^2$, showing how particles in the medium oscillate rapidly as the wave passes. --- These problems illustrate wave velocity as the speed of wave propagation and particle acceleration as the oscillatory motion of particles in the medium.