The fundamental frequency of an open organ pipe that corresponds to a middle C is [f] Hz on the chromatic musical scale. Calculate the length of the open organ pipe If the third harmonics of a closed organ pipe has the same frequency as above, calculate the length of the closed organ pipe
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
The fundamental frequency of an open organ pipe that corresponds to a middle C is [f] Hz on the chromatic musical scale.
Calculate the length of the open organ pipe
If the third harmonics of a closed organ pipe has the same frequency as above, calculate the length of the closed organ pipe
Since, The fundamental frequency of an open organ pipe corresponds to the B above middle C (493.9 Hz on the chromatic musical scale, Assuming that the speed of sound in air is 343 m/s).
We know that the relationship between frequency(f), wavelength() and velocity(v) for an open organ pipe can be given as shown below.
v = λf----(1)
Now, for the open organ pipe, the wavelength of the fundamental is expressed as shown below.
λ= v/f = (343m/s)/(493.9/s) = 0.6945 meter.
So, now the length of this pipe is L/2 = 0.347 m.
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