A 1.70 m long string has a standing wave with 2.00 loops at a frequency of 38.4 Hz.

What is the velocity of the waves in the string?

[tex]\[ v = [?] \, \text{m/s} \][/tex]



Answer :

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]