The length of a string is 344 cm. The string is held fixed at each end. The string vibrates in two sections; i.e., the string has two antin- odes, and the string vibrates at 130 Hz. Find the wavelength answer in m
What is the fundamental frequency? Answer in units of Hz.
To find the wavelength and fundamental frequency of a vibrating string, we can use the formula:
wavelength (λ) = 2 * length (L) / number of antinodes
In this case, the length of the string is given as 344 cm, and the string has two antinodes. Let's first convert the length to meters for consistency:
Length (L) = 344 cm = 3.44 m
Now, we can substitute the values into the formula:
wavelength (λ) = 2 * 3.44 m / 2 = 3.44 m
So, the wavelength of the vibrating string is 3.44 m.
To find the fundamental frequency, we can use the formula:
frequency (f) = speed of wave (v) / wavelength (λ)
Since the speed of the wave is not given, we need to assume it to be the speed of sound, which is approximately 343 m/s.
Substituting the values into the formula:
frequency (f) = 343 m/s / 3.44 m = 100 Hz
Therefore, the fundamental frequency of the vibrating string is 100 Hz.