(Here is the image for my previous question.) The image above represents a stand

Question

(Here is the image for my previous question.)

The image above represents a standing wave in a string with two fixed ends. The standing wave is produced by a vibrator at one end that is vibrating with a frequency of 67.1 Hz.
What is the

1) Number of nodes?:

2) Number of antinodes?:

3) If the length of the string L = 0.700 m, what is the wavelength ? of this standing wave? Show work, include units.

4) Based on the frequency of the vibrator, what is the fundamental frequency of oscillation f1 for this string? Show work, include units.

5) What is the wave speed v? Show work, include units.

6) If the total mass hanging on one end of the string that creates the tension in the string is 0.450 kg, what is the mass density (mass per unit length) ? of the string? Show work, include units.

Explanation / Answer

1) no of nodes = 7

2) no of antindes = 5

3) wavelength = L/3 = 0.233 m

4) f1 = v/L/3 = 3v/L

f0 = v/2L

and v = f1*L/3

==> f0 f1/6 = 11.18 Hz

5) v = 67.1*0.233 =15.656 m/s

6)v = sqrt(T/mu)

mu = T/v^2 = 0.45*9.8/15.656^2 = 0.01799 = 17.99 g/m

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