The range of frequencies, f, is given in Hz. 1Hz = 1/second
To convert this range in units of "seconds per cycle", we need to consider the range of time (in seconds) it takes for the wave to complete one cycle. This time is called period, T.
The period T corresponding to the frequency is calculated as `T = 1/f` .
So for f = 20 Hz, `T = 1/20 = 0.05 ` seconds
For f = 20,000 Hz, `T = 1/20000 =0.00005 ` seconds.
So the range of periods of the musical instruments is from 0.00005 seconds to 0.05 seconds.
It is the exact same range. 20 cycles per second to 20000 cycles per second. Cycles per second is an old unit term. When the International System of Units was adopted in 1960, cycles per second was replaced with hertz.
A cycle per second refers to the number of full wave movements being completed in a second. For a transverse wave, this means how many complete waves and troughs are being generated per second. For sound, which is a longitudinal (compression) wave, the full cycle is a compression and rarefaction. Sound is a vibration, which means that a particular note is created because as object is completing a certain number of cycles per second. So 1000 cycles per second means that the object is vibrating through 1000 complete compressions and rarefactions per second. Or in other words it is vibrating at 1000 hertz.