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A wave on a lake has a cycle length of 0.620 m anda period of 0.300 s. What is the speed of the wave?

Question

A wave on a lake has a cycle length of 0.620 m and a period of 0.300 s. What is the speed of the wave?

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Solution

1. Break Down the Problem

To find the speed of the wave, we need to use the relationship between wave speed, wavelength, and period. The speed v v of a wave is given by the formula: v=dt v = \frac{d}{t} where d d is the distance (wavelength) and t t is the time (period). In this case, the wavelength d d is 0.620 m and the period t t is 0.300 s.

2. Relevant Concepts

We can directly apply the formula for wave speed: v=λT v = \frac{\lambda}{T} where:

  • λ \lambda is the wavelength (cycle length)
  • T T is the period of the wave

3. Analysis and Detail

Now we substitute the values into the formula: v=0.620m0.300s v = \frac{0.620 \, \text{m}}{0.300 \, \text{s}}

4. Verify and Summarize

Perform the division: v=2.0667m/s v = 2.0667 \, \text{m/s} Rounding to three significant figures gives: v2.07m/s v \approx 2.07 \, \text{m/s}

Final Answer

The speed of the wave is approximately 2.07m/s 2.07 \, \text{m/s} .

This problem has been solved

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