A musician plays a C on his piano...?

Question

so that he hears 2 beats/second. Assuming that the tuner is playing a true middle C of 256 Hz, what is the actual frequency he is playing?

2. A harpist plucks a .850 m long string on his harp. The string has a third overtone of 1046.6 Hz. How fast does the vibration travel through the string?

If you can do either, PLEASE help!!! Thanks(:

Answer 1

1. the piano middle C strings are tuned to either 254 Hz or 258 Hz (256 plus or minus 2)

2.  0.85 m * 1046.6 /sec  = 889.6 m/s

(FYI: Hz is per sec.)

I'm not 100% sure about #2.   The only other possible answer is to divide 889.6 by 3 (because of the 3rd overtone).

.

Answer 2

tlbs101 has done #1 already, though the current musical standard puts A at exactly 440 Hz.  For an equal-tempered scale, this puts middle C at about 261 Hz.  The 256 Hz C is a scientific standard for C, not used by musicians.

The third overtone, or fourth harmonic, of 1046.6 Hz means that 4/2 or 2 wavelengths at this frequency fit onto the string.  Each wavelength must therefore be exactly 1/2 of 0.850 m or 0.425 m.  With a frequency of 1046.6 Hz, the speed of the traveling wave is

v = λf

= (0.425 m/cycle)(1046.6 cycle/sec)

= 449 m/sec