AIIMS 2006 Physics Wave Motion MCQ Question

To determine how often the boat bounces up due to the waves, we need to analyze the properties of the wave motion, specifically the wavelength, wave speed, and frequency.

Given Data:

• Wavelength, $\lambda = 100 \, \text{m}$
• Wave speed, $v = 25 \, \text{m/s}$

Step 1: Calculate the Frequency

The frequency $f$ of a wave can be calculated using the formula:

$$f = \frac{v}{\lambda}$$

Substituting in the values we have:

$$f = \frac{25 \, \text{m/s}}{100 \, \text{m}} = 0.25 \, \text{Hz}$$

This frequency means that the wave oscillates 0.25 times per second.

Step 2: Calculate the Time Period

The time period $T$ is the reciprocal of the frequency and represents the time taken for one complete cycle of the wave. The formula for the time period is:

$$T = \frac{1}{f}$$

Substituting the frequency we found:

$$T = \frac{1}{0.25 \, \text{Hz}} = 4 \, \text{s}$$

This indicates that the boat bounces up once every 4 seconds, which corresponds to the time period of the wave.

Conclusion

• Correct Answer: C) 4 s
• The boat bounces up once every $4 \, \text{s}$ due to the wave motion.

Clarification of Incorrect Options:

• A) 2500 s: This is far too long for the time period of the wave. It suggests a misunderstanding of the relationship between frequency and time period.
• B) 75 s: This option is also incorrect and does not relate to the calculated time period or frequency.
• D) 0.25 s: This option represents the frequency, not the time period. The boat does not bounce once every $0.25 \, \text{s}$; that would imply it bounces four times per second, which contradicts our calculation.

Summary

Thus, the correct answer to how often the boat bounces up is indeed C) 4 s, based on the wave's properties and calculations we performed.