Question

You are designing a two-string instrument with metal string 35.0cm long, as shown in the figure(Figure 1) . Both strings are under the same tension. String S₁ has a mass of 8.00g and produces the note middle C (frequency 262Hz ) in its fundamental mode.

Part A

What should be the tension in the string?

Part B

What should be the mass of string S₂ so that it will produce A# (frequency 466Hz ) as its fundamental?

Part C

To extend the range of your instrument, you include a fret located just under the strings, but not normally touching them. How far from the upper end should you put this fret so that when you press S₁ tightly against it, this string will produce C# (frequency 277Hz ) in its fundamental? That is, what is x in the figure?

Part D

If you press S₂ against the fret, what frequency of sound will it produce in its fundamental?

Answer 1