A piano string sounds a middle A by vibrating primarily at 220 Hz. Calculate the

Question

A piano string sounds a middle A by vibrating primarily at 220 Hz. Calculate the string's period and angular frequency, Calculate the period and angular frequency for a soprano singing an A one octave higher, which is twice the frequency of the piano string. If an object on a horizontal, frictionless surface is attached to a spring, displaced, and then released, it will oscillate. If it is displaced 0.120 m from its equilibrium position and released with zero initial speed, then after 0.800 s its displacement is found to be 0.120 m on the opposite side, and it has passed the equilibrium position once during this interval, find the amplitude; the period; the frequency.

Explanation / Answer

13.1)

a)

Time period T = 1/f = 0.004545sec

angular frequency = 2xpixf = 0.02856 rad/sec

b)

frequency = 2x 220 = 440 Hz

period = T = 1/f = 0.00227sec

13.2 )

a)

Amplitude A= 2x0.12 = 0.24m

b)

Period = T = 2x0.8sec = 1.6sec

c)

frequency = 1/T = 0.625 Hz

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