If the third harmonic of a standing wave in a vibrating string is 600 Hz, what is the fundamental frequency?
The first harmonic is the fundamental frquency, by usage nowadays.
Do divide 600 by 3 to get the fundamental (first harmonic).
Oh, harmonics and vibrating strings, how melodious! To find the fundamental frequency, we need to do a little math dance. The fundamental frequency is equal to the frequency of the first harmonic, which is simply the third harmonic divided by three (because the third harmonic is the third multiple of the fundamental frequency). So, if the third harmonic is 600 Hz, the fundamental frequency would be 600 Hz divided by three, which equals... *cue imaginary drumroll* 200 Hz! Ta-da!
The fundamental frequency of a standing wave is inversely proportional to its harmonic number.
To find the fundamental frequency, divide the frequency of the third harmonic by its harmonic number.
Fundamental frequency = Frequency of the third harmonic / Harmonic number
Fundamental frequency = 600 Hz / 3
Fundamental frequency = 200 Hz
Therefore, the fundamental frequency of the standing wave is 200 Hz.
To find the fundamental frequency of a standing wave, you need to know the frequency of one of the harmonics. In this case, we know the frequency of the third harmonic, which is 600 Hz.
The fundamental frequency is the frequency at which the string vibrates when it is divided into equal segments. The formula for calculating the frequency of a harmonic is:
f = n * v / 2L
Where:
- f is the frequency of the harmonic,
- n is the harmonic number (3 in this case),
- v is the velocity of the wave, and
- L is the length of the vibrating string.
Since we are trying to find the fundamental frequency, which corresponds to n = 1, we can rearrange the formula to solve for the velocity:
v = (2L * f) / n
Plugging in the known values, we get:
v = (2L * 600 Hz) / 3
To find the fundamental frequency, we can use:
f1 = v / 2L
Plugging in the newly found velocity and solving for the fundamental frequency:
f1 = ((2L * 600 Hz) / 3) / 2L
The length of the vibrating string cancels out:
f1 = (2 * 600 Hz) / 3
Simplifying this expression:
f1 = 400 Hz
Therefore, the fundamental frequency of the vibrating string is 400 Hz.