The human ear can hear sounds with frequencies from 20 Hz to 20,000 Hz.
Frequencies of sound higher than this are called ultrasound.
Although they cannot be heard, they are used in the technique of ultrasound imaging, for example, to take the image of a fetus in the womb.
The sound waves are reflected off the interface between the fetus and the surrounding fluid.
In order for this to provide information, the wavelength of the sound has to be smaller than the object being observed.
Otherwise the wave passes right around the object.
At the other end of the sound spectrum there are very low frequency sounds.
These can be highly injurious to humans if they have sufficient intensity.
The sounds can cause internal organs to vibrate and eventually rupture, tearing the connective tissue holding the organ in place.
For this reason, there are limits in the workplace as to how intense low frequency sounds can be.
For the following, use 1500 m/s for the speed of sound in biological tissue. Use 343 m/s for the speed of sound in air.
A mass m on a spring (constant k) has a frequency given by
What period corresponds to the lowest frequency a human ear can hear?