Question

A progressive wave of frequency 50 Hz is travelling with velocity 350 m/s through a medium. The change in phase at a given time interval of 0.01 second is

• A. \(\frac{\pi}{4}\ \text{rad}\)
• B. \(\frac{3\pi}{2}\ \text{rad}\)
• C. \(\pi\ \text{rad}\)
• D. \(\frac{\pi}{2}\ \text{rad}\)

Hint:

Phase change over time at a fixed point: \(\Delta \phi = \omega \Delta t = 2\pi f \Delta t\). Frequency in Hz gives cycles per second; multiply by time to get cycles, then by \(2\pi\) for radians.

Answer 1

The Correct Option is C

Step 1: Note what is given.
A wave has frequency $f = 50$ Hz and speed $350$ m/s. At a fixed point we wait a time $\Delta t = 0.01$ s and ask how much the phase changes.

Step 2: Choose the formula.
The phase change with time at a fixed place is $\Delta\phi = 2\pi f \Delta t$. The wave speed is extra information we do not actually need here.

Step 3: Put in the numbers.
$\Delta\phi = 2\pi \times 50 \times 0.01$.

Step 4: Multiply the constants.
$50 \times 0.01 = 0.5$, so $\Delta\phi = 2\pi \times 0.5$.

Step 5: Finish the product.
$2\pi \times 0.5 = \pi$.

Step 6: State the answer.
The phase changes by $\pi$ radians, which is option (C).
\[ \boxed{\Delta\phi = \pi\ \text{rad}} \]