When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by
Y = 0.001 sin 880πt,

Where t is the time (in seconds).

What is the period of the function?

A) sec
B)440 sec
C) sec
D)880 sec
E)88 sec

Question

When tuning a piano, a technician strikes a tuning fork for the A above middle C and sets up a wave motion that can be approximated by ​
Y = 0.001 sin 880πt,
​
Where t is the time (in seconds).
​
What is the period of the function?
​
A) sec 
B)440 sec 
C) sec 
D)880 sec 
E)88 sec

Quizplus · Accepted Answer

The period of a sinusoidal function is the amount of time it takes for one complete cycle. In this case, the function is Y = 0.001 sin 880πt, which represents one complete cycle of a sound wave with a frequency of 880 Hz (the A note above middle C). The equation for the period of a sinusoidal function is T = 2π/ω, where ω is the angular frequency (in radians per second). In this case, ω = 880π, so T = 2π/880π = 1/440 seconds. Converted to scientific notation, this is 2.27 x 10^-3 seconds, which is equivalent to 11.3 milliseconds. Therefore, the period of the function is approximately 11.3 milliseconds, or 1.13 x 10^-2 seconds. The closest answer choice is C, which is 11eacce6_1d5e_ae12_9f49_67599fbfd178_TB7896_11 sec.

When Tuning a Piano, a Technician Strikes a Tuning Fork