Question

The equation of a progressive wave is \(Y = 3sin[π(\frac{t}{3}-\frac{x}{5})+\frac{π}{4}]\) where X and Y are in metre and time in second. Which of the following is correct?

• A. Velocity = \(1.5\) m/s
• B. Amplitude = \(30\) cm
• C. Wavelength = \(10\) m
• D. Frequency = \(0.2\) Hz

Hint:

Compare with Y = A sin(omega t - k x + phi) and find omega, k, wavelength and speed.

Answer 1

The Correct Option is C

Step 1: Use the form with pi factored:
Write the phase as $\pi\left(\dfrac t3-\dfrac x5\right)$. Comparing with $2\pi\left(\dfrac tT-\dfrac x\lambda\right)$, we get $\dfrac{2}{T}=\dfrac13$ and $\dfrac2\lambda=\dfrac15$.

Step 2: Solve:
$T=6$ s, so $f=\dfrac16$ Hz. $\lambda=10$ m. Then $v=f\lambda=\dfrac{10}{6}=1.67$ m/s.

Step 3: Pick:
Only the wavelength of 10 m matches an option, option C.

Final Answer:
The coefficient of x gives k = pi/5, so the wavelength is 10 m. \[ \boxed{\text{(C) }\text{Wavelength}=10\ \text{m}} \]