Question

type the correct answer in each box. use numerals instead of words.
a tuning fork vibrates with a frequency of 440 hertz (cycles/second). when the tuning fork is struck, it produces a change in the normal air pressure in the room.
function p represents this situation, where p(t) is the change in pressure, in pascals, relative to the normal air pressure in the room as a function of time, t, in seconds, after the tuning fork is struck.
p(t) = 5 sin(880πt)
what are the domain and the range within the context of this situation?
the domain of the function is t ≥
the range of the function is ≤ p(t) ≤ .

Explanation:

Step1: Define domain context

Time starts at strike, so $t \geq 0$.

Step2: Analyze sine function range

The $\sin(x)$ function has range $-1 \leq \sin(x) \leq 1$.

Step3: Scale sine function by 5

Multiply all parts by 5: $5(-1) \leq 5\sin(880\pi t) \leq 5(1)$, so $-5 \leq p(t) \leq 5$.

Answer:

The domain of the function is $t \geq 0$
The range of the function is $-5 \leq p(t) \leq 5$