Question

A sphere of mass M is supported by a string that passes over a pulley at the end of a horizontal rod of length L . The string makes an angle θ with the rod. The fundamental frequency of the standing waves in the portion of the string above the rod is f. Find the mass of the portion of the string above the rod. (Use any variable or symbol stated above along with the following as necessary: g.)

Answer 1

length of string vibrating=half wave length.
You need to find tension
Summing moments about the fixed end of the rod.
-MgL+tension*L*(sin(90-theta))=0

Now look at stringl forces on the pulley
tension=Mg
so tension*L(sin(90-theta)-1)=0
Now we need to covert L to length of string
lengthstring=L/cos(90-theta)
or L=lengthstring*cos( )
tension*lengtthstring*cos( )(sin( )=0
now to the wave equation: f*wavelength=speed
we can relate speed to tension and mass/length, and wavelength to the lengthstsring, and from that find mass/length.

Can you handle it from here? (check my work)

Answer 2

Yes! :) Thank you so much for your help!