A standing wave is vibrating on a string attached at one end to a mechanical oscillator. The other end of the string passes over a pulley and is attached to a mass that holds the string under tension. The distance between the end of the oscillator and the top of the pulley is 2.23 m. The wavelength of the wave on the string is 89.2 cm.

What is the harmonic number n of the mode of vibration of the standing wave?

With standing waves of this sort, the ends are physically constrained to be nodes for the harmonic. To determine what harmonic is present, what you want to observe is how many antinodes are on the string because each one represents lambda/2 and a half-wavelength is the fundamental.

Since lambda = 0.892 m, lambda/2 = 0.446 m

To find the harmonic, divide the string length by lambda/2: