Solved: CALC Figure P16.75 shows the pressure fluctuation

Chapter 16, Problem 83CP

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QUESTION:

Figure P16.83 shows the pressure fluctuation \(p\) of a non sinusoidal sound wave as a function of \(x\) for \(t=0\). The wave is traveling in the \(+x \text {-direction }\).

(a) Graph the pressure fluctuation \(p\) as a function of \(t\) for \(x=0\). Show at least two cycles of oscillation.

(b) Graph the displacement \(y\) in this sound wave as a function of \(x\) at \(t=0\). At \(x=0\), the displacement at \(t=0\) is zero. Show at least two wavelengths of the wave.

(c) Graph the displacement \(y\) as a function of \(t\) for \(x=0\). Show at least two cycles of oscillation.

(d) Calculate the maximum velocity and the maximum acceleration of an element of the air through which this sound wave is traveling.

(e) Describe how the cone of a loudspeaker must move as a function of time to produce the sound wave in this problem.

Questions & Answers

QUESTION:

Figure P16.83 shows the pressure fluctuation \(p\) of a non sinusoidal sound wave as a function of \(x\) for \(t=0\). The wave is traveling in the \(+x \text {-direction }\).

(a) Graph the pressure fluctuation \(p\) as a function of \(t\) for \(x=0\). Show at least two cycles of oscillation.

(b) Graph the displacement \(y\) in this sound wave as a function of \(x\) at \(t=0\). At \(x=0\), the displacement at \(t=0\) is zero. Show at least two wavelengths of the wave.

(c) Graph the displacement \(y\) as a function of \(t\) for \(x=0\). Show at least two cycles of oscillation.

(d) Calculate the maximum velocity and the maximum acceleration of an element of the air through which this sound wave is traveling.

(e) Describe how the cone of a loudspeaker must move as a function of time to produce the sound wave in this problem.

ANSWER:

Step 1 of 5

(a) Since the pressure as a function is a triangular wave, the pressure as a function of time will also be a triangular wave. And since the given pressure at x = 0, and t = 0 is zero, the pressure as a function of time at x=0 will also start from zero.

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