Astronauts visiting Planet X have a 2.5 m long string whose mass is 5 g. They ti

Question

Astronauts visiting Planet X have a 2.5 m long string whose mass is 5 g. They tie the string to a support, stretch it horizontally over a pulley 2 m away, and hang a 1 kg mass on the free end. Then they attempt to produce standing waves on the string. They are successful for vibration frequencies of 64 Hz and 80 Hz but at no frequencies between those two. If they now allow the mass to oscillate freely as a pendulum (small angles), at what frequency (Hz) will it do so? (You may treat the hanging mass as a point mass, but you may not ignore the mass of the string.)

Explanation / Answer

since fundmental frequency is given by

fn=nf

where f=fundmental frequency

therfore

fn+1-fn=f

f=80-64=16 Hz

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