Math Problem Statement
A student observes two transverse waves with different frequencies. Wave A has a frequency of 5 waves per second, and Wave B has a frequency of 10 waves per second.
Which statement best describes the pattern between frequency and wavelength for these waves? A.Wave B has a longer wavelength than Wave A. B.Wave B has a shorter wavelength than Wave A. C.Both waves have the same wavelength. D.The wavelength is not affected by the frequency.
Solution
The correct answer is:
B. Wave B has a shorter wavelength than Wave A.
Explanation:
The relationship between frequency () and wavelength () is given by the wave equation: where is the wave speed.
Assuming both waves travel at the same speed, a higher frequency will correspond to a shorter wavelength, and a lower frequency will correspond to a longer wavelength. Since Wave B has a higher frequency (10 waves per second) than Wave A (5 waves per second), it will have a shorter wavelength than Wave A.
Would you like further details or have any questions?
Related Questions:
- How does wave speed affect the relationship between frequency and wavelength?
- If Wave A’s frequency doubled, how would its wavelength change?
- What is the relationship between energy and frequency for transverse waves?
- How can we calculate the wavelength if we know wave speed and frequency?
- Why is wavelength inversely proportional to frequency in wave equations?
Tip: For waves in the same medium, increasing frequency always results in a decrease in wavelength.
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Math Problem Analysis
Mathematical Concepts
Wave frequency
Wavelength
Inverse relationship between frequency and wavelength
Formulas
v = f * λ
Theorems
Inverse relationship of frequency and wavelength in a given medium
Suitable Grade Level
Grades 8-10
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