Question

The equation of a progressive wave is given by \(y = 6cos(100t-4x)\) where \(y\) is in \(μ\text{m}\), \(x\) in metre and \(t\) in second. The ratio of the maximum particle velocity to the velocity of wave is

• A. \(1.5\times 10^{-5}\)
• B. \(2.0\times 10^{-6}\)
• C. \(2.4\times 10^{-5}\)
• D. \(2.8\times 10^{-6}\)

Hint:

Maximum particle velocity is A times omega and the wave velocity is omega over k.

Answer 1

The Correct Option is C

Step 1: Use the formula directly
The ratio is $\dfrac{A\omega}{\omega/k} = Ak$.

Step 2: Substitute
$Ak = 6\times10^{-6}\times4 = 24\times10^{-6}$.

Step 3: Result
$2.4\times10^{-5}$.

Step 4: Check
The angular frequency cancels, so the ratio is simply the amplitude times the wave number. It is small because the amplitude is much smaller than the wavelength.

Final Answer:
The ratio is 2.4 x 10^-5. This is option (C). \[ \boxed{\text{(C) }2.4\times10^{-5}} \]