To solve for the velocity of the waves in the string, we first need to understand the relationship between the wavelength, frequency, and velocity.
Here are the steps for the calculation:
1. Find the Wavelength:
When a string has a standing wave with loops (or nodes), the wavelength [tex]\(\lambda\)[/tex] can be calculated using the following relationship:
[tex]\[
\lambda = \frac{2 \times \text{length}}{\text{loops}}
\][/tex]
Given:
- Length of the string = 1.70 meters
- Number of loops = 2.00
Substituting these values into the equation:
[tex]\[
\lambda = \frac{2 \times 1.70 \, \text{m}}{2.00} = 1.70 \, \text{m}
\][/tex]
2. Calculate the Velocity:
The velocity [tex]\(v\)[/tex] of a wave is given by the equation:
[tex]\[
v = \text{frequency} \times \text{wavelength}
\][/tex]
Given:
- Frequency = 38.4 Hz
- Wavelength [tex]\(\lambda\)[/tex] = 1.70 meters
Substituting these values into the equation:
[tex]\[
v = 38.4 \, \text{Hz} \times 1.70 \, \text{m} = 65.28 \, \text{m/s}
\][/tex]
Therefore, the velocity of the waves in the string is:
[tex]\[
v = 65.28 \, \text{m/s}
\][/tex]
