Problem: The basic equation connecting wave speed v, wavelength? and frequency f isThe wave speed in a stretched string depends on the string's tension T and mass per unit length? (also called the "linear mass density") with the equationAssume you have the following intermediate (i.e., significant figures may be incorrectly stated) experimental results :L =0.812 ? 0.019 mf1 =29.02 ? 1.45 HzT =5.08 N (exact)1. Use the above results to calculate the fractional uncertainty in the wave speed ?v:2. Use the above results to calculate the fractional uncertainty in the linear mass density ??:3. Then calculate the absolute uncertainty in the linear mass density ??:4. Finally, state the linear mass density with its uncertainty using correct significant figures (include units):

FREE Expert Solution

1.

The fractional uncertainty in the wave speed = uncertainty in the wave speed/the value of the wave speed

= (1.45+0.019)/47.13 = 0.03117

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Problem Details

The basic equation connecting wave speed v, wavelength? and frequency f is

The wave speed in a stretched string depends on the string's tension T and mass per unit length? (also called the "linear mass density") with the equation

Assume you have the following intermediate (i.e., significant figures may be incorrectly stated) experimental results :


L =0.812 ? 0.019 m
f1 =29.02 ? 1.45 Hz
T =5.08 N (exact)


1. Use the above results to calculate the fractional uncertainty in the wave speed ?v:


2. Use the above results to calculate the fractional uncertainty in the linear mass density ??:


3. Then calculate the absolute uncertainty in the linear mass density ??:


4. Finally, state the linear mass density with its uncertainty using correct significant figures (include units):

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