Q110 / 150 · MHT CET 2026 (16 April Shift 1) · Physics
The equation of wave motion is $Y = 6\sin\left(12\pi t - 0.02\pi x + \dfrac{\pi}{3}\right)$ where x is in metre and time in second. The velocity of the wave is
- A$200$ m/s
- B$300$ m/s
- C$400$ m/s
- Correct answerD$600$ m/s
Solution
The standard equation of a travelling wave is $Y = A\sin(\omega t - kx + \phi)$.
Comparing the given equation $Y = 6\sin\left(12\pi t - 0.02\pi x + \dfrac{\pi}{3}\right)$ with the standard equation, we get:
$\omega = 12\pi$ rad/s
$k = 0.02\pi$ rad/m
The velocity of the wave is given by $v = \dfrac{\omega}{k}$.
Substituting the values:
$v = \dfrac{12\pi}{0.02\pi} = \dfrac{12}{0.02} = 600$ m/s.
Answer: $600$ m/s
Comparing the given equation $Y = 6\sin\left(12\pi t - 0.02\pi x + \dfrac{\pi}{3}\right)$ with the standard equation, we get:
$\omega = 12\pi$ rad/s
$k = 0.02\pi$ rad/m
The velocity of the wave is given by $v = \dfrac{\omega}{k}$.
Substituting the values:
$v = \dfrac{12\pi}{0.02\pi} = \dfrac{12}{0.02} = 600$ m/s.
Answer: $600$ m/s
Hence, the correct answer is option: 'D'.