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)
Responses

λA = λB

λ A = λ B

λA = 9λB

λ A = 9 λ B

λA = 1/9 λB

λ A = 1/9 λ B

λA = 1/3 λB

λ A = 1/3 λ B

Answer 1

To relate the wavelengths of the two waves based on their frequencies, we can use the wave equation:

\[ v = f \lambda \]

where \( v \) is the speed of the wave, \( f \) is the frequency, and \( \lambda \) is the wavelength. Since both waves are traveling through the same medium, they have the same speed \( v \).

Given that:

- The frequency of Wave A, \( f_A = 9 f_B \) (where \( f_B \) is the frequency of Wave B).

We can rearrange the wave equation for both waves:

For Wave A:
\[ v = f_A \lambda_A \]
\[ \lambda_A = \frac{v}{f_A} \]

For Wave B:
\[ v = f_B \lambda_B \]
\[ \lambda_B = \frac{v}{f_B} \]

Since \( f_A = 9 f_B \), we can substitute:

\[ \lambda_A = \frac{v}{9 f_B} \]

Now, we can express \( \lambda_B \):

\[ \lambda_B = \frac{v}{f_B} \]

Now, we can find the relationship between \( \lambda_A \) and \( \lambda_B \):

\[ \lambda_A = \frac{v}{9 f_B} = \frac{1}{9} \cdot \frac{v}{f_B} = \frac{1}{9} \lambda_B \]

Thus, the relationship between the wavelengths is:

\[ \lambda_A = \frac{1}{9} \lambda_B \]

Based on the response options you provided, the correct answer is:

**λA = 1/9 λB**