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Answer :
To find the velocity of the waves in the string, we can follow these steps:
1. Understand the scenario: The string is 1.70 meters long and has a standing wave with 2 loops. A standing wave with 2 loops means there is one full wavelength on the string, because each loop represents half of a wavelength.
2. Calculate the wavelength: Since there are 2 loops forming one full wavelength on a 1.70-meter-long string, the wavelength is divided equally across the loops. Therefore, the wavelength is:
[tex]\[
\text{Wavelength} = \frac{\text{Length of the string}}{\text{Number of loops}} = \frac{1.70 \, \text{m}}{2} = 0.85 \, \text{m}
\][/tex]
3. Calculate the velocity of the waves: The velocity of waves can be calculated using the formula:
[tex]\[
\text{Velocity} = \text{Frequency} \times \text{Wavelength}
\][/tex]
Given that the frequency of the wave is 38.4 Hz, we can substitute the values to calculate the velocity:
[tex]\[
\text{Velocity} = 38.4 \, \text{Hz} \times 0.85 \, \text{m} = 32.64 \, \text{m/s}
\][/tex]
So, the velocity of the waves in the string is 32.64 meters per second.
1. Understand the scenario: The string is 1.70 meters long and has a standing wave with 2 loops. A standing wave with 2 loops means there is one full wavelength on the string, because each loop represents half of a wavelength.
2. Calculate the wavelength: Since there are 2 loops forming one full wavelength on a 1.70-meter-long string, the wavelength is divided equally across the loops. Therefore, the wavelength is:
[tex]\[
\text{Wavelength} = \frac{\text{Length of the string}}{\text{Number of loops}} = \frac{1.70 \, \text{m}}{2} = 0.85 \, \text{m}
\][/tex]
3. Calculate the velocity of the waves: The velocity of waves can be calculated using the formula:
[tex]\[
\text{Velocity} = \text{Frequency} \times \text{Wavelength}
\][/tex]
Given that the frequency of the wave is 38.4 Hz, we can substitute the values to calculate the velocity:
[tex]\[
\text{Velocity} = 38.4 \, \text{Hz} \times 0.85 \, \text{m} = 32.64 \, \text{m/s}
\][/tex]
So, the velocity of the waves in the string is 32.64 meters per second.
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