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:

In wave motion, if speed increases and frequency remains constant, wavelength increases proportionally.

Answer 1

The Correct Option is C

The relationship between wave speed \(v\), frequency \(f\), and wavelength \(\lambda\) is given by: \[ v = f\lambda \] When a wave travels from one medium to another (e.g., shallow to deep water), its frequency remains constant. Therefore, any change in speed will directly affect the wavelength. If speed doubles (\(v' = 2v\)), and \(f\) remains the same: \[ v' = f\lambda' \Rightarrow \lambda' = \frac{v'}{f} = \frac{2v}{f} = 2\lambda \] Hence, the wavelength also doubles.

Answer 2

Step 1: Recall the wave relationship
The speed \(v\), frequency \(f\), and wavelength \(\lambda\) of a wave are related by:
\[ v = f \lambda \]

Step 2: Understand the change in speed
- When a wave moves from shallow to deeper water, its speed doubles:
\[ v' = 2v \]
- Frequency \(f\) remains constant because it depends on the source.

Step 3: Calculate new wavelength
Using \(v' = f \lambda'\), we get:
\[ \lambda' = \frac{v'}{f} = \frac{2v}{f} = 2 \lambda \]

Step 4: Final answer
The wavelength will be doubled.