Period and Frequency of Sound Waves as Shown on the Screen
Problem Statement
Period and Frequency of Sound Waves as Shown on the Screen
Problem Statement
To investigate the properties of sound in a laboratory, a device (an electromagnetic tuning fork) that maintains a constant electrical oscillation was used to generate a sound of a specific pitch. The frequency f of this device is expressed in Hz and represents the number of times the medium vibrates per second.
Now, the sound waves emitted by this device were captured by a microphone and displayed on a computer screen. The time from the highest point of a wave (a crest) to the next crest is called the period T of the sound wave. The unit for the period T is the second s.
The following relationship holds between the frequency f and the period T.
f=T1When the period T of this device was measured, its value was expressed as T=t1, where t is a variable. Find the value of the frequency f in this case, and determine the natural number that satisfies the following input format.
Constraints
- t=400 s−1
Input Format
Let A be the numerical value of the frequency f. Enter the value of A as a natural number.
Solution
Explanation
Relationship Between Frequency and Period
The frequency f (number of oscillations per second) and the period T (time taken for one oscillation) are inversely proportional to each other. The relationship given in the problem is as follows:
f=T1Substituting Expressions
Substitute T=t1 for the period T into the equation.
f=t11=tThis shows that the value of the frequency f is equal to the value of t.
Numerical Calculation
Since t=400 according to the constraints, the frequency f is as follows:
f=400 HzTherefore, the value of A for the frequency f is 400.
The natural number to be entered is 400.