MHT CET · Physics · Oscillations
The equation of simple harmonic wave is given as \(\mathrm{y}=5 \sin \frac{\pi}{2}(100 \mathrm{t}-\mathrm{x})\), where ' \(\mathrm{x}\) '
and ' \(\mathrm{y}\) ' are in metre and time in second. The period of the wave is
- A \(0 \cdot 02 \mathrm{~s}\)
- B \(5 \mathrm{~s}\)
- C \(25 \mathrm{~s}\)
- D \(0 \cdot 04 \mathrm{~s}\)
Answer & Solution
Correct Answer
(D) \(0 \cdot 04 \mathrm{~s}\)
Step-by-step Solution
Detailed explanation
(B)
\(\begin{array}{l}
\mathrm{y}=5 \sin \frac{\pi}{2}(100 \mathrm{t}-\mathrm{x}) \\
\mathrm{y}=\operatorname{Asin}(\omega \mathrm{t}-\mathrm{kx}) \\
\omega=\frac{2 \pi}{\mathrm{T}} \\
\mathrm{T}=\frac{2 \pi}{100} \\
\Rightarrow \mathrm{T}=0.06
\end{array}\)
Hence, the correct option is (B)
\(\begin{array}{l}
\mathrm{y}=5 \sin \frac{\pi}{2}(100 \mathrm{t}-\mathrm{x}) \\
\mathrm{y}=\operatorname{Asin}(\omega \mathrm{t}-\mathrm{kx}) \\
\omega=\frac{2 \pi}{\mathrm{T}} \\
\mathrm{T}=\frac{2 \pi}{100} \\
\Rightarrow \mathrm{T}=0.06
\end{array}\)
Hence, the correct option is (B)
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