1. Problem 1: Wave Velocity in a String Given: A string under tension carries a wave with wavelength $\lambda = 0.5$ m and frequency $f = 200$ Hz. Unknown: 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: $$v = 200 \times 0.5 = 100 \text{ m/s}$$ Step 3: Interpretation: The wave travels along the string at 100 m/s. This velocity is the speed of the wave itself, not the particles. 2. Problem 2: Particle Acceleration in a Sound Wave Given: A particle in a sound wave oscillates with amplitude $A = 0.01$ m and angular frequency $\omega = 400 \text{ rad/s}$. Unknown: Maximum particle acceleration $a_{max}$. Step 1: Use the formula for maximum acceleration in simple harmonic motion: $$a_{max} = \omega^2 \times A$$ This formula calculates the peak acceleration of particles oscillating in the wave. Step 2: Substitute the values: $$a_{max} = 400^2 \times 0.01 = 160000 \times 0.01 = 1600 \text{ m/s}^2$$ Step 3: Interpretation: Particles in the medium oscillate with a maximum acceleration of 1600 m/s$^2$, showing the rapid changes in motion within the wave. These problems illustrate that wave velocity describes how fast the wave propagates through the medium, while particle acceleration describes the oscillatory motion of particles within the wave.