Concept explainers
Sound Vibrations A tuning fork is struck, producing a pure tone as its tines vibrate. The vibrations are modeled by the function
where v(t) is the displacement of the tines in millimeters at time t seconds.
- (a) Find the period of the vibration.
- (b) Find the frequency of the vibration, that is, the number of times the fork vibrates per second.
- (c) Graph the function v.
(a)
To find: The period of the vibration for the given function.
Answer to Problem 78E
One period of the function
Explanation of Solution
Given:
The vibration are modeled by the function
Formulas used:
The sine curve
Calculation:
Rewrite the function.
That is,
Here,
The period of the wave is computed as follows,
Therefore, one period of the function
(b)
To find: The frequency of the vibration. That is, the number of times for k vibrates per second.
Answer to Problem 78E
The frequency of the vibration is 440.
Explanation of Solution
Calculation:
From part (a), One period of the function
That is, one vibration takes time
Thus, there are 440 vibration per second.
(c)
To sketch: The graph of the function v.
Explanation of Solution
Use the online graphing calculator to draw the function as shown below in Figure 1.
From Figure 1, it is observed that the function has maximum value occurs at
Chapter 5 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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