Question

Question #5c99f

Answer 1

The period of the fundamental is 0.022sec.

The frequency of the fourth harmonic is 180Hz.

The frequency of the fifth harmonic is 225Hz.

There are 6 nodes in the fifth harmonic.

Explanation:

With out seeing the graphic we will assume that the fundamental frequency is 45Hz and that the standing wave is set up in a string with both ends fixed.

The period is equal to one over the frequency, so that the period of the fundamental frequency will be

`1/45sec^-1=0.022sec`

The fourth and fifth harmonics are just multiples of the fundamental harmonic, following the formula
`F_n`=nF

So that the fourth harmonic will be
`F_4=4*45=180Hz`

And the fifth harmonic will be

`F_5=5*45=225Hz`

Standing waves have an alternating pattern of nodes (N) and antinodes (A).
Standing waves in strings with both ends fixed have a node at each end of the string.
Simply "fill in" the pattern to find the number of nodes for each frequency .

The fundamental goes: N-A-N
The second harmonic goes: N-A-N-A-N.
and so on
The fifth harmonic looks like: N-A-N-A-N-A-N-A-N-A-N

That is a total of 6 nodes in the fifth harmonic.