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Solved: CALC (a) Defend the following statement: “In a
Chapter 16, Problem 58P(choose chapter or problem)
CALC (a) Defend the following statement: "In a sinusoidal sound wave, the pressure variation given by Eq. (16.4) is greatest where the displacement given by Eq. (16.1) is zero." (b) For a sinusoidal sound wave given by Eq. (16.1) with amplitude \(A=10.0 \mu \mathrm{m}\) and wavelength \(\lambda=0.250 \mathrm{~m}\), graph the displacement and pressure fluctuation
as functions of
at time \(t=0\). Show at least two wavelengths of the wave on your graphs. (c) The displacement
in a nonsinusoidal sound wave is shown in Fig. P16.58 as a function of
for \(t=0\). Draw a graph showing the pressure fluctuation
in this wave as a function of
at \(t=0\). This sound wave has the same \(10.0-\mu m\) amplitude as the wave in part (b). Does it have the same pressure amplitude? Why or why not? (d) Is the statement in part (a) necessarily true if the sound wave is not sinusoidal? Explain your reasoning.
Equation Transcription:
Text Transcription:
A=10.0 um
lambda=0.250 m
t=0
t=0
10.0-um
y(um)
Questions & Answers
QUESTION:
CALC (a) Defend the following statement: "In a sinusoidal sound wave, the pressure variation given by Eq. (16.4) is greatest where the displacement given by Eq. (16.1) is zero." (b) For a sinusoidal sound wave given by Eq. (16.1) with amplitude \(A=10.0 \mu \mathrm{m}\) and wavelength \(\lambda=0.250 \mathrm{~m}\), graph the displacement and pressure fluctuation
as functions of
at time \(t=0\). Show at least two wavelengths of the wave on your graphs. (c) The displacement
in a nonsinusoidal sound wave is shown in Fig. P16.58 as a function of
for \(t=0\). Draw a graph showing the pressure fluctuation
in this wave as a function of
at \(t=0\). This sound wave has the same \(10.0-\mu m\) amplitude as the wave in part (b). Does it have the same pressure amplitude? Why or why not? (d) Is the statement in part (a) necessarily true if the sound wave is not sinusoidal? Explain your reasoning.
Equation Transcription:
Text Transcription:
A=10.0 um
lambda=0.250 m
t=0
t=0
10.0-um
y(um)
ANSWER:
Solution 58P
Problem (a)
Step 1:
For a sinusoidal wave, the pressure variation decreases as the displacement is greater. Therefore pressure is greater when displacement is zero. Hence the statement given is valid.
Problem (b)
To plot displacement and pressure variation
Step 1:
Displacement
----(1)
Pressure variation
or
(
=
)