The pressure in a traveling sound wave is given by the equation - p - 1-50 Pa sin- - 0-900 m-1 x - 315 s-1 t -Find the a pressure amplitude- b frequency- c wavelength- and d speed of the wave-

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Standard IX

Physics

Effect of Pressure on Speed of Sound in Gases

The pressure ...

Question

The pressure in a traveling sound wave is given by the equation
$Δ p = (1.50 P a) sin π [(0.900 m^{- 1}) x - (315 s^{- 1}) t]$ .
Find the (a) pressure amplitude, (b) frequency, (c) wavelength, and (d) speed of the wave.

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Solution

(a) The amplitude of a sinusoidal wave is the numerical coefficient of the sine (or cosine) function : $p_{m} = 1.50 P a$ .
(b) We identify $k = 0.9 π$ and $ω = 315 π$ (in SI units), which leads to $f = ω / 2 π = 158 H z$ .
(c) We also obtain $λ = 2 π / k = 2.22 m$ .
(d) The speed of the wave is $v = ω / k = 350 m / s$

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The pressure in a traveling sound wave is given by the equationΔp=(1.50Pa)sinπ[(0.900 m−1)x−(315 s−1)t].Find the (a) pressure amplitude, (b) frequency, (c) wavelength, and (d) speed of the wave.

(a) The amplitude of a sinusoidal wave is the numerical coefficient of the sine (or cosine) function : pm=1.50Pa.(b) We identify k=0.9π and ω=315π (in SI units), which leads to f=ω/2π=158 Hz.(c) We also obtain λ=2π/k=2.22 m.(d) The speed of the wave is v=ω/k=350 m/s

The pressure in a traveling sound wave is given by the equation
$Δ p = (1.50 P a) sin π [(0.900 m^{- 1}) x - (315 s^{- 1}) t]$ .
Find the (a) pressure amplitude, (b) frequency, (c) wavelength, and (d) speed of the wave.