Question

two similar waves are traveling through the same medium. wave a has a frequency that is 9 times that of wave b. (1 point)
$\lambda_a = 1/3 \lambda_b$
$\lambda_a = 1/9 \lambda_b$
$\lambda_a = 9\lambda_b$
$\lambda_a = \lambda_b$

Explanation:

Step1: Recall wave speed formula

For waves in the same medium, speed \( v \) is constant. The formula is \( v = f\lambda \), where \( f \) is frequency and \( \lambda \) is wavelength. So \( v_A = v_B \), which means \( f_A\lambda_A = f_B\lambda_B \).

Step2: Relate frequencies

Given \( f_A = 9f_B \). Substitute into the speed equation: \( 9f_B \cdot \lambda_A = f_B \cdot \lambda_B \).

Step3: Solve for \( \lambda_A \)

Divide both sides by \( 9f_B \) (assuming \( f_B
eq 0 \)): \( \lambda_A = \frac{f_B\lambda_B}{9f_B} = \frac{1}{9}\lambda_B \).

Answer:

\( \lambda_A = 1/9 \lambda_B \) (the option with this expression)