How we can check the frequency in Hertz in our home electric current?
A frequency counter is the most accurate way. As stated above
some digital multimeters include this feature, but stand alone
frequency counters are also available.
Another way is to use an oscilloscope and measure the period of
one cycle, then calculate the frequency as the reciprocal of the
period you measured.
Another way is to use a multiple tuning fork frequency meter.
These devices have perhaps a dozen tuning forks tuned to different
frequencies (with the 60 Hz fork in the center, lower frequency
forks to the left, and higher frequency forks to the right) and an
electromagnetic excitation coil. The tuning fork(s) closest in
frequency to the powerline will vibrate and the others will remain
stationary, allowing you to read the frequency. They are a bit
course in their measurement, but usually can identify differences
of about 0.1 Hz.
However, if your home is powered from the national power grid
(not a local generator) the frequency is required to be 60 Hz to a
precision that a clock synchronized to the power line will never be
more then 10 seconds fast or slow of the correct time, although the
line frequency might be high or low for short periods as much as a
couple Hz.