A standing wave in a pipe with a length L=1.2 ~m is described by y(x, t)=y_0 sin [(2 π / L) x] sin [(2 π / L) x+π / 4] Based on above information, which one of the following statements is incorrect. (Speed of sound in air is 300 ~m ~s^-1 )-

Correct answer: (D) The frequency of the fundamental mode of vibrations is 137.5 ~Hz. (2 π)/(λ) x=(2 π)/L x ∴ λ=L=1.2 ~m at x=0, x=L, y=0 v=v/(λ)=300/1.2=250 ~Hz

Q69 / 90 · KVPY 2012 (SB/SX) · Physics

A standing wave in a pipe with a length $L=1.2 \mathrm{~m}$ is described by $y(x, t)=y_{0} \sin [(2 \pi / L) x] \sin [(2 \pi / \mathrm{L}) x+\pi / 4]$ Based on above information, which one of the following statements is incorrect. (Speed of sound in air is $300 \mathrm{~m} \mathrm{~s}^{-1}$ )-

A
The pipe is closed at hoth ends
B
The wavelength of the wave could be $1.2 \mathrm{~m}$
C
There could be a node at $\mathrm{x}=0$ and antinode at $\mathrm{x}=\mathrm{L} / 2$
Correct answer
D
The frequency of the fundamental mode of vibrations is $137.5 \mathrm{~Hz}$

Solution

$\begin{array}{l} \frac{2 \pi}{\lambda} \mathrm{x}=\frac{2 \pi}{\mathrm{L}} \mathrm{x} \\ \therefore \lambda=\mathrm{L}=1.2 \mathrm{~m} \\ \text { at } \mathrm{x}=0, \mathrm{x}=\mathrm{L}, \mathrm{y}=0 \\ \mathrm{v}=\frac{\mathrm{v}}{\lambda}=\frac{300}{1.2}=250 \mathrm{~Hz} \end{array}$

Hence, the correct answer is option: 'D'.

A standing wave in a pipe with a length $L=1.2 \mathrm{~m}$ is described by $y(x, t)=y_{0} \sin [(2 \pi / L) x] \sin [(2 \pi / \mathrm{L}) x+\pi / 4]$ Based on above information, which one of the following statements is incorrect. (Speed of sound in air is $300 \mathrm{~m} \mathrm{~s}^{-1}$ )-

Solution

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