A standing wave in a pipe with a length L = 1.2 m is described by y(x, t) = y _0 \sin[({2\pi}/L) x] \sin[({2\pi}/L)x +\pi/4]Based on above information, which one of the following statement is incorrect . ( Speed of sound in air is 300 m.s^{-1}).

Correct Answer is : The frequency of the fundamental mode of vibrations is 137.5 Hz

The pipe is closed at both ends

The wavelength of the wave could be 1.2 m

There could be a node at x = 0 and antinode at x = L/2

The frequency of the fundamental mode of vibrations is 137.5 Hz

KVPY SX SB Exam 2012 Question Paper

Question : 98 of 120

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A standing wave in a pipe with a length L = 1.2 m is described by

y(x, t) = y _0 \sin[({2π}/L) x] \sin[({2π}/L)x +π/4]

Based on above information, which one of the following statement is incorrect.
( Speed of sound in air is 300 m.s

^{-1}

Solution:

{2\π}/\λx={2\π}/\L x

∴λ = L =1.2m

at x = 0, x = L, y = 0

\υ=\v/\λ=300/1.2=250\Hz

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