To compare the wavelengths of waves A and B, we can use the relationship between wave speed (v), frequency (f), and wavelength (λ), which is given by the formula:
\[ v = f \cdot \lambda \]
Since both waves are traveling at the same speed, we can set the speed of wave A equal to the speed of wave B:
\[ v_A = v_B \]
Because \( v = f \cdot \lambda \), we can write:
\[ f_A \cdot \lambda_A = f_B \cdot \lambda_B \]
Given that the frequency of wave A is 3 times that of wave B:
\[ f_A = 3 f_B \]
Substituting this into the equation, we get:
\[ (3 f_B) \cdot \lambda_A = f_B \cdot \lambda_B \]
Now, we can divide both sides by \( f_B \) (assuming \( f_B \neq 0 \)):
\[ 3 \lambda_A = \lambda_B \]
Now, we can solve for the wavelength of wave A:
\[ \lambda_A = \frac{\lambda_B}{3} \]
Thus, the comparison of the wavelengths is:
\[ \lambda_A = \frac{1}{3} \lambda_B \]
So the correct response is:
λA = 1/3 λB.