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Expression for Standing Waves

In sound wave...

Question

In sound waves,a displacement node is a pressure antinode snd vice versa.Explain why?

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Solution

A node is a point where the amplitude of vibration is the minimum and pressure is the maximum. On the other hand, an antinode is a point where the amplitude of vibration is the maximum and pressure is the minimum.

Therefore, a displacement node is nothing but a pressure antinode, and vice versa

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Similar questions

Q. Assertion - In a sound wave, a displacement node is a pressure antinode and vice versa.
Reason - Displacement node is point of minimum displacement.

Q. Explain why (or how):
(a) in a sound wave, a displacement node is a pressure antinode and vice versa,
(b) bats can ascertain distances directions, nature and sizes of the obstacles without any "eyes"
(c) a violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,
(d) solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and
(e) the shape of a pulse gets distorted during propagation in a dispersive medium.

Q. Assertion :When a closed organ pipe vibrates, the pressure of the gas at the closed end remains constant. Reason: In a stationary-wave system, displacement nodes are pressure antinodes, and displacement antinodes are pressure nodes.

Q. The equation of a longitudinal standing wave due to superposition of the progressive waves produced by two sources of sound is

s = - 20 sin (10 π x) \times sin (100 π t)

s

is the displacement from mean position measured in

m m, x

is in meters and

t

is in seconds. The specific gravity of the medium is

10^{- 3}

. Density of water

= 10^{3} k g / m^{3}

. Find:
(a) Wavelength, frequency and velocity of the progressive waves.
(b) Bulk modulus of the medium and the pressure amplitude.
(c)Minimum distance between pressure antinode and a displacement antinode
(d)intensity at the displacement node.

Q. Explain analytically how stationary waves are formed. What are nodes and antinodes? Show that the distance between two adjacent nodes or antinodes is

\frac{λ}{2}

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