# trig formula for oscillations per second

• Aug 8th 2011, 06:04 AM
furor celtica
trig formula for oscillations per second
A tuning fork is vibrating. The displacement, y centimetres, of the tip of one of the prongs from its rest position after t seconds is given by
y= 0.1sin(100 000t
Find :
a. the greatest displacement and the time at which it first occurs,
b. the time taken for one complete oscillation of the prong,
c. the number of complete oscillations per second of the tip of the prong

I answered a. and b. correctly with the following responses:
a. y= 0.1 cm., t= 0.000 9 s.
b. 0.003 6 s.

For c. I answered 277 (complete oscillation p/s) taking the answer to b.
1/0.0036 = 277.8 (correct to 1 d.p.)
Which makes 277 complete oscillations per second.

However the correct answer is given to be 278.
Why is this?
• Aug 8th 2011, 06:07 AM
Siron
Re: trig formula for oscillations per second
I think 277,8 is approximately 278.
• Aug 8th 2011, 06:14 AM
furor celtica
Re: trig formula for oscillations per second
complete oscillations per second
• Aug 8th 2011, 09:59 PM
mr fantastic
Re: trig formula for oscillations per second
Quote:

Originally Posted by furor celtica
complete oscillations per second

Assuming 277.8 is correct, then your answer is correct and the book is wrong. A classic case of where rounding for context overrides the mathematical rules for rounding.