To demonstrate the relationship between the length, frequency, and resonance, six metal strips of different lengths and equal thickness are placed on a mechanical driver-oscillator. The oscillator is driven by a sinusoidal signal from a function generator (see Fig 1). The audience observes a sequence of strips under resonance as the frequency is increased. The range of resonant frequencies for all six strips is between 17 and 65 Hz.

Materials:

• Model SF-9324 Mechanical Vibrator
• Fredrikson Function Generator
• Two Banana Cables

Demo:
To set up the demo, connect the Fredrikson function generator to the mechanical vibrator using two banana cables. Increase the output voltage to ~3.0V and slowly increase the frequency until the metal strips begin vibrating. Avoid increasing the voltage over 3.0V, the amplitudes of the oscillations will be too large and the strips will hit the base.

The 6 strips on the top of the mechanical vibrator are all of equal thicknesses. The frequencies listed below will exhibit resonance for each respective metal strip.

A     —–     13.5cm     —–     18.30 Hz
B     —–     12.5cm     —–     20.75 Hz
C     —–     11.5cm     —–     25.30 Hz
D     —–     9.5cm       —–     37.23 Hz
E     —–     8.5cm       —–     46.30 Hz
F     —–     7.5cm       —–     62.76 Hz

Explanation:

When the function generator is turned on, the mechanical vibrator will oscillate the center shaft of the apparatus at the set frequency. When the frequency of the function generator reaches a resonant frequency for one of the strips of metal, it will oscillate at maximum amplitude while the other strips will barely move.

Since each strip has a fixed end and a free end, the fundamental frequency can be described by:

where lambda is the wavelength of the fundamental frequency and L is the length of the metal strip.

Each frequency, f, will produce an oscillation in the metal strips, exhibiting resonance when the fundamental frequency is reached for each strip. Since each L is different, then the fundamental resonant frequency wavelength will also be different, changing with lambda by the following equation:

where v is the velocity of the wavelength in the medium.

Notes:

• A video camera is required for big auditoriums

Written by Phoenix Gallagher