Vibration with frequency 6.00x10^2 Hz are established on a 1.33m length of string that is clamped at both ends. The speed wave on the string is 4.00x10^2 m/s. How far from either end of the string does the first node occur?
To find the distance from either end of the string where the first node occurs, we can use the formula for the wavelength of a wave on a string:
wavelength = (2L) / n
where:
- wavelength is the distance between two consecutive nodes or antinodes
- L is the length of the string
- n is an integer representing the number of nodes or antinodes
We are given:
- frequency = 6.00x10^2 Hz
- length of the string (L) = 1.33 m
- wave speed = 4.00x10^2 m/s
The wavelength can be calculated using the formula:
wavelength = wave speed / frequency
wavelength = (4.00x10^2 m/s) / (6.00x10^2 Hz)
wavelength = 0.67 m
The first node represents a half-wavelength, so it occurs at one-fourth of a full wavelength from either end of the string.
distance from either end = (wavelength / 4)
distance from either end = (0.67 m) / 4
distance from either end = 0.17 m
Therefore, the first node occurs at a distance of 0.17 m from either end of the string.