Question

If the speed of a wave doubles as it passes from shallow water into deeper water, its wavelength will be

• A. unchanged
• B. halved
• C. doubled
• D. quadrupled

Hint:

If wave speed changes but frequency remains constant, wavelength changes in the same ratio as speed.

Answer 1

The Correct Option is C

Step 1: Use wave relation.
Wave speed is given by:
\[ v = f\lambda \]
Step 2: Frequency remains constant.
When a wave enters a new medium, the frequency does not change because it is decided by the source.
Step 3: Compare old and new speed.
If speed doubles:
\[ v' = 2v \]
Step 4: Find the new wavelength.
\[ v' = f\lambda' \Rightarrow 2v = f\lambda' \]
But \(v = f\lambda\), so:
\[ 2f\lambda = f\lambda' \Rightarrow \lambda' = 2\lambda \]
Final Answer:
\[ \boxed{\text{(C) doubled}} \]