Question
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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 = 1/3 λB
λ A = 1/3 λ B
λA = 1/9 λB
λ A = 1/9 λ B
λA = 9λB
λ A = 9 λ B
λA = λB
λ A = λ B
Answers
GPT-4o mini
To solve the relationship between the wavelengths of Wave A and Wave B given their frequencies, we can use the wave equation:
\[ v = f \cdot \lambda \]
where:
- \( v \) is the wave speed (which is the same for both waves since they are traveling through the same medium),
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.
Given that Wave A has a frequency that is 9 times that of Wave B, we can express this relationship mathematically:
Let:
- \( f_B \) be the frequency of Wave B,
- \( f_A = 9 f_B \) be the frequency of Wave A.
Since both waves have the same speed \( v \), we can write the wave equations for both waves:
For Wave A:
\[ v = f_A \cdot \lambda_A \]
For Wave B:
\[ v = f_B \cdot \lambda_B \]
Setting these equal to one another gives us:
\[ f_A \cdot \lambda_A = f_B \cdot \lambda_B \]
Substituting \( f_A = 9 f_B \) into the equation, we have:
\[ 9 f_B \cdot \lambda_A = f_B \cdot \lambda_B \]
We can divide both sides by \( f_B \) (assuming \( f_B \neq 0 \)):
\[ 9 \lambda_A = \lambda_B \]
Now, solving for \( \lambda_A \):
\[ \lambda_A = \frac{1}{9} \lambda_B \]
Thus, the correct response is:
\[ \lambda_A = \frac{1}{9} \lambda_B \]
\[ v = f \cdot \lambda \]
where:
- \( v \) is the wave speed (which is the same for both waves since they are traveling through the same medium),
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.
Given that Wave A has a frequency that is 9 times that of Wave B, we can express this relationship mathematically:
Let:
- \( f_B \) be the frequency of Wave B,
- \( f_A = 9 f_B \) be the frequency of Wave A.
Since both waves have the same speed \( v \), we can write the wave equations for both waves:
For Wave A:
\[ v = f_A \cdot \lambda_A \]
For Wave B:
\[ v = f_B \cdot \lambda_B \]
Setting these equal to one another gives us:
\[ f_A \cdot \lambda_A = f_B \cdot \lambda_B \]
Substituting \( f_A = 9 f_B \) into the equation, we have:
\[ 9 f_B \cdot \lambda_A = f_B \cdot \lambda_B \]
We can divide both sides by \( f_B \) (assuming \( f_B \neq 0 \)):
\[ 9 \lambda_A = \lambda_B \]
Now, solving for \( \lambda_A \):
\[ \lambda_A = \frac{1}{9} \lambda_B \]
Thus, the correct response is:
\[ \lambda_A = \frac{1}{9} \lambda_B \]