Question

An anchored boat is rocked by waves whose crests are 100 m apart and whose velocity is 25 m/s. How often do the crests reach the boat?

• A. 0.35 s
• B. 4 s
• C. 75 s
• D. 2500 s

Answer 1

The correct option is B

4 s

Step 1: Given data.

$$\begin{gathered} wavlength=100m \\ velocity=25m/s \end{gathered}$$

Step 2: Finding the time period of the crests to reach the boat.

1. The wavelength and frequency of a sound wave are related mathematically as:
2. $$\begin{gathered} Thevelocityofsound=frequency\times wavelength \\ \Rightarrow V=\vartheta \times \lambda \\ \Rightarrow V=\frac{1}{T}\times \lambda \left[\vartheta =\frac{1}{T}\right] \\ \Rightarrow T=\frac{\lambda }{V} \\ \Rightarrow T=\frac{100}{25}s \\ \Rightarrow T=4s \end{gathered}$$
3. where $\lambda$ = wavelength, v = velocity, T = time period and $\vartheta$ = frequency.
4. Therefore, the time period of the crests to reach the boat is 4 s

Hence, option (b) is correct.