Two progressive sound waves move in opposite directions and superpose to form a stationary wave.
Which statement describes an antinode of this stationary wave?
Correct Answer: \( \boxed{\mathrm{C}} \)
An antinode is a point on a stationary wave where the oscillation amplitude is greatest.
Nodes have zero amplitude, while antinodes have maximum amplitude.
Therefore, the correct answer is (C).
The diagram shows a stationary wave on a stretched spring at an instant in time.
Two particles on the spring, \( P \) and \( Q \), are shown.
Which statement about the vibrations of \( P \) and \( Q \) is correct?
Correct Answer: \( \boxed{\mathrm{D}} \)
Points \( P \) and \( Q \) lie between the same pair of nodes, so they are in the same loop of the stationary wave.
All particles within the same loop oscillate in phase, although their amplitudes may differ depending on their positions.
They also have the same frequency and period.
Therefore, the correct answer is (D).
A pipe of length \(100\,\mathrm{cm}\) is open at both ends. A loudspeaker situated at one end of the pipe can emit sound of different wavelengths.
Which wavelength can produce a stationary wave in the pipe?
Correct Answer: \( \boxed{\mathrm{A}} \)
For a pipe open at both ends, the allowed wavelengths satisfy
\( L=\dfrac{n\lambda}{2} \), where \(n=1,2,3,\ldots\)
With \(L=100\,\mathrm{cm}\),
\( \lambda=\dfrac{2L}{n}=\dfrac{200}{n}\,\mathrm{cm} \)
Testing the options, only \( \lambda=50\,\mathrm{cm} \) corresponds to \(n=4\), an integer.
Therefore, the correct answer is (A).
