# Standing Waves

## Background Reading:

Page 1, Page 2, Page 3, Page 4.

## Procedure

• Attach the mass hanger to the free end of the string over the pulley. Make sure that the string is parallel to the lab bench.
• Turn on the tuning fork vibrator and add some mass to the hanger. Do NOT supply more than 7 volts DC to the vibrator!
• You should be able to see six or seven normal modes of vibration. The fundamental requires about 1.5 kg on the hook. The higher normal modes are obtained by decreasing the mass on the hook. Eventually, the mass of the empty hook will limit the number of normal modes that you can observe.
• Determine the load mass on the string, the wavelength of oscillation, and the normal mode (= number of nodes - 1).
• Repeat for as many different normal modes as possible.

## Error analysis

• Start with the formula from the prelab relating linear frequency, string tension, linear mass density, and wavelength. Write a formula for the linear frequency of vibration in terms of measured quantities only. (Hint: There are five measured quantities.)
• For the error in the hanging mass, estimate how much mass must be added to or subtracted from the hook before you notice a difference in the behavior of the vibrating string.
• Propagate the error in f from the errors in the measured quantities for each normal mode seen.
• Is the manufacturer's linear frequency f=80 Hz within your error bounds? In other words, can you verify that the tuning fork is operating as advertized?
• If you wanted to decrease f and you could only improve one of the measured quantities, which one should it be? In other words, which of the measured quantities has the largest fractional error?
• Identify at least two sources of statistical error.
• Identify at least two sources of systematic error.

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