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)

OЛA = 9 Л B

Л A =1/9 Л B

ЛA = ЛB

Л A =1/3 Л B

Answer 1

The wavelength and frequency of a wave are related by the equation:

\[ v = f \lambda \]

where:
- \( v \) is the speed of the wave,
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.

If Wave A has a frequency (\( f_A \)) that is 9 times that of Wave B (\( f_B \)), we can express this relationship as:

\[ f_A = 9 f_B \]

If the waves are traveling through the same medium, they have the same wave speed (\( v \)). Therefore, we can set up the following equations for the wavelengths:

1. For Wave A:
\[ v = f_A \lambda_A \]
2. For Wave B:
\[ v = f_B \lambda_B \]

Since \( f_A = 9 f_B \), we can substitute into the equation for Wave A:

\[ v = 9 f_B \lambda_A \]

Since both waves have the same speed, we can equate these:

\[ 9 f_B \lambda_A = f_B \lambda_B \]

Dividing both sides by \( f_B \) (assuming \( f_B \) is not zero):

\[ 9 \lambda_A = \lambda_B \]

This implies:

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

So, the correct answer is:

**Л A = 1/9 Л B**.