Apiano string sounds a middle a by vibrating primarily at 220 hz. a)calculate its period. b)calculate its angular frequency. c)calculate the period for a soprano singing a "high a," two octaves up, which is four times the frequency of the piano string. d)calculate the angular frequency for a soprano singing a "high a," two octaves up, which is four times the frequency of the piano string.

a) 4.5 ms

The period of a wave is given by:

where f is the frequency.

For the note in this problem, f = 220 Hz, so the period of the wave is

b) 1381.6 rad/s

The angular frequency is given by:

where f is the frequency.

In this problem, f = 220 Hz, so the angular frequency is

c) 1.1 ms

The frequency of the "high A" is four times the frequency of the piano string, so

And so, its period is

d) 5526.4 rad/s

The angular frequency is given by:

where f is the frequency.

For this note, f = 880 Hz, so the angular frequency is

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