Cracking the SAT Physics Subject Test

fn =

Tip

You can remember nodes

as areas of “no displacement.”

Antinodes are the

opposite of that.

These are the harmonic (or resonant) frequencies. A standing wave will form on
a string if we create a traveling wave whose frequency is the same as a resonant
frequency. The first standing wave, the one for which the harmonic number, n, is 1,
is called the fundamental standing wave. From the equation for the harmonic
frequencies, we see that the nth harmonic frequency is simply n times the
fundamental frequency.

fn = nf 1

Likewise, the nth harmonic wavelength is equal to λ 1 divided by n. Therefore, if

we know the fundamental frequency (or wavelength), we can determine all the
other resonant frequencies and wavelengths.

7. A string of length 12 m that’s fixed at both ends supports a
   standing wave with a total of 5 nodes. What are the harmonic
   number and wavelength of this standing wave?

Here’s How to Crack It

First, draw a picture.