Wave A has a wavelength of 2 meters and a frequency of 1.5 Hz Calculate the wave's speed. Wave B has a frequency of 18 Hz in the same medium. What is Wave B's speed? Calculate Wave B's wavelength. So, as \( f \) increases in the same medium, \( \lambda \)

**Step 1: Calculate the speed of Wave A** The relationship between wave speed \( v \), wavelength \( \lambda \), and frequency \( f \) is given by: \[ v = \lambda f \] For Wave A: \[ \lambda_A = 2 \text{ m}, \quad f_A = 1.5 \text{ Hz} \] Thus, the speed of Wave A is: \[ v_A = 2 \text{ m} \times 1.5 \text{ Hz} = 3 \text{ m/s} \] **Step 2: Determine the speed of Wave B** Since both waves travel in the same medium, they have the same speed. Therefore: \[ v_B = v_A = 3 \text{ m/s} \] **Step 3: Calculate the wavelength of Wave B** For Wave B, we use the same formula: \[ \lambda_B = \frac{v_B}{f_B} \] Given: \[ v_B = 3 \text{ m/s}, \quad f_B = 18 \text{ Hz} \] The wavelength of Wave B is: \[ \lambda_B = \frac{3 \text{ m/s}}{18 \text{ Hz}} = \frac{1}{6} \text{ m} \approx 0.167 \text{ m} \] **Step 4: Relationship between \( f \) and \( \lambda \)** Since the speed \( v \) in a medium is constant, the formula \( v = \lambda f \) implies that the wavelength \( \lambda \) is inversely proportional to the frequency \( f \). Therefore, as \( f \) increases in the same medium, \( \lambda \) decreases.