To analyze the given information about the two waves, let's summarize the data in the table:
-
Wave 1:
- Wavelength = 5 meters
- Frequency = 200 Hz
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Wave 2:
- Wavelength = 3 meters
- Frequency = 300 Hz
Using the relationship between wavelength (\( \lambda \)), frequency (\( f \)), and wave speed (\( v \)), which is defined by the equation:
\[ v = f \times \lambda \]
We can calculate the wave speed for each wave.
For Wave 1: \[ v_1 = f_1 \times \lambda_1 = 200 , \text{Hz} \times 5 , \text{m} = 1000 , \text{m/s} \]
For Wave 2: \[ v_2 = f_2 \times \lambda_2 = 300 , \text{Hz} \times 3 , \text{m} = 900 , \text{m/s} \]
Conclusion:
From the calculations, we observe the following:
- Wave 1 has a greater wavelength and a lower frequency while traveling at a speed of 1000 m/s.
- Wave 2 has a shorter wavelength and a higher frequency while traveling at a speed of 900 m/s.
The conclusion we can draw from this is that:
- The wave with a longer wavelength (Wave 1) has a lower frequency and travels faster than the wave with a shorter wavelength (Wave 2), which, despite having a higher frequency, travels at a slower speed.
This illustrates the relationship between wavelength, frequency, and wave speed, confirming that as frequency increases, wavelength decreases when wave speed is relatively constant. However, in this case, the speeds differ due to the specific characteristics of each wave.
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