What should be the length of an organ pipe, closed at one end if the fundamental frequency is 200 Hz?
Use v = 345 m/sec
What is the frequency of the next harmonic?
To find the length of an organ pipe closed at one end given its fundamental frequency, we can use the formula:
L = (v / 4f)
where:
L = length of the pipe
v = speed of sound in air (345 m/sec)
f = fundamental frequency
In this case, the fundamental frequency is 200 Hz. So we can substitute the values into the formula:
L = (345 m/sec) / (4 * 200 Hz)
L = 0.8625 m
Therefore, the length of the organ pipe is approximately 0.8625 meters.
To find the frequency of the next harmonic, we need to consider the relationship between the fundamental frequency (f1) and the frequency of the nth harmonic (fn):
fn = nf1
where:
fn = frequency of the nth harmonic
f1 = fundamental frequency
n = number of the harmonic
In this case, we're looking for the frequency of the next harmonic, which means n = 2. Substituting the values:
fn = 2 * 200 Hz
fn = 400 Hz
Therefore, the frequency of the next harmonic is 400 Hz.