Question

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=1/9λB
lambda sub A is equal to 1 ninth lambda sub b

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

λA=1/3λB
lambda sub A is equal to 1 third lambda sub b

λA=3λB
lambda sub A is equal to 3 lambda sub b
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Answer 1

To solve the problem, we can use the relationship between the speed of a wave (v), its frequency (f), and its wavelength (λ):

\[ v = f \cdot \lambda \]

Let \( f_A \) and \( f_B \) be the frequencies of waves A and B, respectively, and let \( \lambda_A \) and \( \lambda_B \) be their wavelengths.

Given that wave A has a frequency that is 3 times that of wave B:

\[ f_A = 3 f_B \]

Since both waves are traveling at the same speed (v), we can write the equations for the two waves:

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

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

Since both equations equal \( v \), we can set them equal to each other:

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

Substituting \( f_A = 3 f_B \) into the equation:

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

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

\[ 3 \lambda_A = \lambda_B \]

Now we can solve for \( \lambda_A \):

\[ \lambda_A = \frac{1}{3} \lambda_B \]

Thus, the wavelengths compare as:

\[ \lambda_A = \frac{1}{3} \lambda_B \]

The correct response is:

**λA = 1/3λB**
(lambda sub A is equal to 1 third lambda sub b)