The fundamental frequency of a string fixed at both ends is 325 Hz. How long does it take for a wave to travel the length of this string?
The time for one cycle is 1/325 sec. The time to go to one end (1/2 wavelength away) is one half that time.
yes it is
To find the time it takes for a wave to travel the length of a string, we need to consider the wavelength and the wave speed.
The formula for the speed of a wave on a string is given by:
v = f * λ
Where:
v is the wave speed,
f is the frequency of the wave, and
λ is the wavelength.
In this case, we are given the fundamental frequency of the string, which is 325 Hz. The fundamental frequency corresponds to the first harmonic, which has one complete wavelength along the length of the string.
The formula for the wavelength of the first harmonic on a string fixed at both ends is:
λ = 2L
Where:
λ is the wavelength, and
L is the length of the string.
Since the string is fixed at both ends, the wavelength of the first harmonic is twice the length of the string.
Therefore, substituting the values into the formula, we have:
v = f * λ
v = 325 Hz * 2L
To find the time it takes for a wave to travel the length of the string, we can rearrange the formula as follows:
t = d / v
Where:
t is the time,
d is the distance (length of the string), and
v is the wave speed.
Substituting the values, we have:
t = 2L / (325 Hz * 2L)
t = 1 / (325 Hz)
Therefore, the time it takes for a wave to travel the length of the string is 1/325 seconds, or approximately 0.0031 seconds.