Question

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

• A. Unchanged
• B. Doubled
• C. Quadrupled
• D. Halved

Answer 1

The correct option is B

Doubled

Step 1: Given

Initial speed of wave: $v_1=v$

New speed of wave: $v_2=2v$

Frequency of wave: $f$

Step 2: Formula Used

$v=f\lambda$

Step 3: Find the new wavelength

The frequency of a wave remains constant as it passes through one medium to another. Equate frequency in both cases and substitute the ratio of velocity and wavelength for frequency.

$$\begin{gathered} f_1=f_2 \\ \Rightarrow \frac{v_1}{{\lambda }_1}=\frac{v_2}{{\lambda }_2} \\ \Rightarrow \frac{v}{\lambda }=\frac{2v}{{\lambda }_2} \\ \Rightarrow {\lambda }_2=\frac{2v}{v}\lambda \\ \Rightarrow {\lambda }_2=2\lambda \end{gathered}$$

Hence, the frequency gets doubled if the velocity is doubled.

Therefore, option (B) is the correct answer.