trig formula for oscillations per second

[furor celtica]

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?

 

[mmm4444bot]

c. the number of complete oscillations per second of the tip of the prong

The phrase "complete oscillations" means some Whole number of oscillations.


1/0.0036 = 277.8 (correct to 1 [decimal place])

Which makes 277 complete oscillations per second.

However the correct answer is given to be 278.

Why is this?

If we round the decimal number 277.8 to the nearest Whole number, we get 278.

.

 

[Deleted member 4993]

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?

If I were your instructor - I would have given you full credit. Since the problem asks for specifically complete oscillations - I think the correct answer is 277.

 

[mmm4444bot]

I think the correct answer is 277.

I'm thinking differently.

If the exercise were to have asked instead, "What is the complete number of oscillations within the first second?", then I would agree with 277.

What they have actually asked for is a generalized rate.

Let's look at the error margins for 277 versus 278 over time.

In 90 seconds, for example, there are exactly 25,000 oscillations.

If we say that the rate is 277 oscillations per second, then 90*277 is off by 70 oscillations.

If we say that the rate is 278 oscillations per second, then 90*278 is off by 20 oscillations.

In 900 seconds, the error with rate 277 is 700 oscillations, and the error with rate 278 is 200 oscillations, et cetera.

It seems to me that, as a general rate-per-second of "complete oscillations", the value 278 is a better answer because the error is smaller.