Question

Two waves are traveling at the same speed. Wave A has a frequency that is 3 times that of wave B .

How do their wavelengths compare?

(1 point)
Responses

λA=19λB
lambda sub A is equal to 1 ninth lambda sub b

λA=13λB
lambda sub A is equal to 1 third lambda sub b

λA=3λB
lambda sub A is equal to 3 lambda sub b

λA=λB

Answer 1

To compare the wavelengths of the two waves, we can use the relationship between wave speed (v), frequency (f), and wavelength (λ), which is given by the equation:

\[ v = f \cdot \lambda \]

Given that both waves travel at the same speed (v), we can set up the equations for waves A and B.

Let:
- \( f_B \) = frequency of wave B
- \( f_A = 3f_B \) = frequency of wave A (since wave A has a frequency that is 3 times that of wave B)

Using the equation for each wave:

For wave A:
\[ v = f_A \cdot \lambda_A \]

For wave B:
\[ v = f_B \cdot \lambda_B \]

Since both waves travel at the same speed (v), we can set the equations equal to each other:

\[ f_A \cdot \lambda_A = f_B \cdot \lambda_B \]

Now substituting \( f_A = 3f_B \):

\[ 3f_B \cdot \lambda_A = f_B \cdot \lambda_B \]

Now, we can divide both sides by \( f_B \) (assuming \( f_B \neq 0 \)):

\[ 3\lambda_A = \lambda_B \]

Now, solving for \( \lambda_A \):

\[ \lambda_A = \frac{\lambda_B}{3} \]

This means that the wavelength of wave A is one third that of wave B:

Therefore, the correct response is:

**λA=13λB (lambda sub A is equal to 1 third lambda sub b)**