- #1

Von Neumann

- 101

- 4

**Problem:**

Determine the quantity of resonant frequencies that a 1024 Hz tuning fork will have in a 1m long tube with an adjustable water level. Find the length of the air column for each frequency. Assume the speed of sound is 344m/s.

**Solution:**

The resonant frequencies are odd integer multiples of the fundamental so,

f=(2n-1)f'

(where f' is the 1st resonant, n the number of nodes, and f is the nth resonant frequency)

f=(2n-1)v/[itex]\lambda[/itex]

=(2n-1)v/(4l)

= [(n-1/2)v]/(2l)

Solving for l,

l=[(n-1/2)v]/(2f)

Substituting values of n into the equation until l > 1m,

n=1

l=8.4cm

n=2

l=25.2cm

n=3

l=42.0cm

n=4

l=58.8cm

n=5

l=75.6cm

n=6

l=92.4cm

Plugging in n=7 yields a length of 1.08 m, so the wave is no longer within the tube. Therefore there are 6 resonant frequencies.

Is this correct?

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