The experimental procedure was carried out, and tension versus wavelength squared was plotted. The slope of the graph was found to be 2.2 Nm-2, and the frequency was determined to be 41.7 Hz.Determine the mass per unit length of the string, expressing answer in SI units, to 3 significant figuresEntering numbers in scientific notation: Example: 1.45 x 10-9 should be entered as 1.45E-9

The mass per unit length (linear density) of the string can be determined using the formula for the speed of a wave on a stretched string:

v = sqrt(T/μ)

where: v is the speed of the wave, T is the tension in the string, and μ is the mass per unit length (linear density) of the string.

The speed of the wave can also be determined using the formula:

v = fλ

where: f is the frequency of the wave, and λ is the wavelength of the wave.

From the given information, we know that the slope of the tension versus wavelength squared graph is 2.2 Nm-2. This is equivalent to the tension in the string divided by the square of the wavelength (T/λ^2). Therefore, we can write:

T/λ^2 = 2.2 Nm-2

We also know that the frequency of the wave is 41.7 Hz. Therefore, we can write:

v = fλ = 41.7Hz * λ

Substituting the expression for T/λ^2 into the formula for the speed of the wave gives:

v = sqrt(2.2 Nm-2 * λ^2) = sqrt(2.2) * λ = 1.48 * λ

Setting this equal to the expression for the speed of the wave in terms of the frequency and wavelength gives:

1.48 * λ = 41.7Hz * λ

Solving for λ gives:

λ = 1.48/41.7 = 0.0355 m

Substituting this value back into the expression for T/λ^2 gives:

T = 2.2 Nm-2 * (0.0355 m)^2 = 0.00277 N

Finally, substituting the values for T and v into the formula for the linear density gives:

μ = T/v^2 = 0.00277 N / (1.48 * 0.0355 m)^2 = 0.00119 kg/m

Therefore, the mass per unit length of the string is approximately 0.00119 kg/m, to three significant figures.