A sonometer wire is 0.80 m long between its bridges, and its tension comes from a load hanging over…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A sonometer wire is long between its bridges, and its tension comes from a load hanging over a pulley, as in the figure. With a load of the wire, sounding its fundamental, gives beats per second with a tuning fork. With a load of it again gives beats per second with the same fork. Take .
- What is the frequency of the fork?
- What is the frequency of the wire with the load?
- What is the linear mass density of the wire?
- What load makes the wire sound in unison with the fork?
- The load is made of metal of density . It is now hung fully under water, of density . How many beats per second does the wire give with the fork?
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. The two loads give two wire notes, apart, with the fork in the middle. Their ratio is fixed by the square root of the loads.
Step 1. The two notes (a, b). and . So , and . The fork is between them: .
Step 2. Linear density (c). From :
Step 3. Unison (d). .
Step 4. Under water (e). The tension falls to , so the note falls to . The beats are .
Answer: (a) . (b) . (c) . (d) . (e) .
Watch out. The load for unison is not the average of the two loads, . The frequency goes as the square root of the load, so the right load is a little less.
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