Statement-1: In a plane progressive sound wave, a displacement node always corresponds to a pressure antinode, and a displacement antinode always corresponds to a pressure node. Statement-2: The press

Question

Statement-1: In a plane progressive sound wave, a displacement node always corresponds to a pressure antinode, and a displacement antinode always corresponds to a pressure node.

Statement-2: The pressure amplitude of a sound wave is directly proportional to the displacement amplitude, the angular frequency, and the speed of sound in the medium.

TestHub · Accepted Answer

Statement-1 is true. In a sound wave, displacement and pressure variations are $9 0^{\circ}$ out of phase. Where displacement is maximum (antinode), the particles momentarily come to rest, leading to minimum pressure change (node). Where displacement is zero (node), the particles are moving with maximum velocity, causing maximum compression or rarefaction (antinode) in pressure.

Statement-2 is true. For a displacement wave $s = s_{0} sin (k x - ω t)$ , the excess pressure wave is $P = P_{0} cos (k x - ω t)$ , where the pressure amplitude $P_{0} = B k s_{0}$ . Since $k = ω / v$ (where $v$ is the speed of sound and $B$ is the bulk modulus), we have $P_{0} = B (ω / v) s_{0}$ . Also, $v = B / ρ$ , so $B = ρ v^{2}$ . Substituting this, $P_{0} = (ρ v^{2}) (ω / v) s_{0} = ρ v ω s_{0}$ . Thus, $P_{0}$ is directly proportional to $s_{0}$ , $ω$ , and $v$ .

Both statements are true, but Statement-2 explains the relationship between amplitudes and wave properties, not the phase relationship between displacement and pressure nodes/antinodes.

Physics - Sound Wave Question with Solution | TestHub

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