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Chapter 9: Problem 3

You're sitting in a small boat on the open ocean, rising and falling with each passing wave crest. How could you measure the frequency of the wave passing under your boat?

Short Answer

Expert verified
Count the wave crests passing the boat over a set time and divide the number of crests by the time interval.

Step by step solution

01

- Understand the Problem

Determine what needs to be measured: the frequency of the wave passing under your boat. Frequency is defined as the number of wave crests passing a point per unit time.
02

- Identify Equipment

Have a stopwatch or any time-measuring device available to measure the time accurately.
03

- Count the Wave Crests

Start the stopwatch when a wave crest passes under the boat. Count the number of wave crests that pass under the boat for a certain duration, for example, 30 seconds or 1 minute.
04

- Measure the Time Interval

After counting the desired number of wave crests, stop the stopwatch. Record the total time elapsed during the counting.
05

- Calculate the Frequency

Use the formula for frequency: \[ \text{Frequency} (f) = \frac{\text{Number of Wave Crests}}{\text{Time Interval}} \] Substituting the values, you get the frequency in waves per second (Hertz).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

wave motion
Wave motion refers to the transfer of energy through a medium via waves. Imagine you are sitting in a small boat on the ocean. As the waves pass, they lift the boat up and then allow it to fall. This is wave motion in action.

Waves can be classified into different types, such as:
  • Transverse Waves: These are waves where the motion of the medium is perpendicular to the direction of the wave. Think of ocean waves or the ripples on a pond when you throw a stone.
  • Longitudinal Waves: Here, the motion of the medium is in the same direction as the wave travels. Sound waves traveling through air are a good example of this.
In the case of the boat on the ocean, you are experiencing transverse waves. The surface of the water moves up and down while the energy of the wave moves horizontally. This motion can be harnessed to measure various properties of waves, such as frequency.
frequency calculation
Frequency is a measure of how many wave crests pass a given point per unit of time. It is measured in Hertz (Hz), where 1 Hz equals one wave crest passing per second.

To calculate the frequency of the waves passing under your boat, follow these steps:
  • Use a stopwatch to measure the time.
  • Count the number of wave crests that pass under your boat in a specific time period (e.g., 30 seconds or 1 minute).
  • Record the total time taken.
  • Use the formula \( f = \frac{N}{T} \) where f is the frequency, N is the number of wave crests, and T is the time interval.
For example, if 15 wave crests pass under your boat in 30 seconds, the frequency calculation will be:

\[f = \frac{15}{30} = 0.5\ Hz\]

This means the frequency of the waves is 0.5 Hz, or one wave crest every 2 seconds.
time measurement
Accurate time measurement is crucial when calculating wave frequency. To ensure you have the precise frequency, follow these guidelines:
  • Use a reliable stopwatch.
  • Start counting wave crests as soon as the first crest passes under the boat.
  • Continue counting for a set period, like 30 seconds or 1 minute, without looking away or stopping.
  • Stop the stopwatch as soon as the set period ends and note the total time elapsed.
Time measurement helps eliminate inaccuracies and ensures that the frequency calculation reflects the true nature of the wave motion you are observing. Whether you are in a small boat on the ocean or conducting experiments in a lab, getting the time measurement right is crucial for accurate and reliable frequency results.

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Most popular questions from this chapter

As you swim away from shore at the ocean, you go through a region where the wave crests are breaking and then reach a more distant region where they don't break. What distinguishes the two regions?
See all solutions

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