Standing Wave A standing wave with amplitude 0.6 is graphed at several times t as shown in the figure. If the vibration has a frequency of 20 Hz, find an equation of the form y(x, t) = A sin αx cos βt that models this wave.
To find: The equation of the standing wave amplitude 0.6 and vibrating frequency 20 Hz.
Answer to Problem 5P
The equation of the wave is
Explanation of Solution
Given:
The equation has the form
Formula used:
Velocity of the wave is
Calculation:
The amplitude of the wave is 0.6.
From the figures it can be observed that the period of the wave is p = 2 and the wavelength
It is given that the equation has the form
The value of
Therefore,
The value of
The velocity of the wave is calculated as follows.
Therefore,
Hence, calculate
Therefore,
It is given that amplitude is
Using all the above values the equation of the wave is
Chapter 7 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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