a) 4.5 ms
The period of a wave is given by:
[tex]T=\frac{1}{f}[/tex]
where f is the frequency.
For the note in this problem, f = 220 Hz, so the period of the wave is
[tex]T=\frac{1}{f}=\frac{1}{220 Hz}=4.5\cdot 10^{-3} s = 4.5 ms[/tex]
b) 1381.6 rad/s
The angular frequency is given by:
[tex]\omega=2 \pi f[/tex]
where f is the frequency.
In this problem, f = 220 Hz, so the angular frequency is
[tex]\omega=2 \pi (220 Hz)=1381.6 rad/s[/tex]
c) 1.1 ms
The frequency of the "high A" is four times the frequency of the piano string, so
[tex]f=4 \cdot 220 Hz=880 Hz[/tex]
And so, its period is
[tex]T=\frac{1}{f}=\frac{1}{880 Hz}=1.1\cdot 10^{-3} s=1.1 ms[/tex]
d) 5526.4 rad/s
The angular frequency is given by:
[tex]\omega=2 \pi f[/tex]
where f is the frequency.
For this note, f = 880 Hz, so the angular frequency is
[tex]\omega=2 \pi (880 Hz)=5526.4 rad/s[/tex]
