Question

Two waves, each having a frequency of 100 H${}_z$ and a wavelength of 2.0 cm, are travelling in the same direction on a string. What is the phase difference between the waves (a) if the second wave was produced 0.015 s later than the first one at the same place, what would be the resultant amplitude? [Given individual amplitudes = 2.0 mm]

• A. 4 mm
• B. 2 mm
• C.
• D. zero

Answer 1

The correct option is D

zero

Phase diagram method can be used here but for that we need to calculate the phase difference.

$\Delta \varphi =2\pi \frac{\Delta t}{T}$

Here $\Delta t=0.015s$

$T_1$ which is the time period =$\frac{1}{f}$

$T=\frac{1}{100}$

So $\Delta \varphi =2\pi \frac{0.015}{\frac{1}{100}}=3\pi =2\pi +\pi$ as $2\pi$ is the period, the effective phase difference is $\pi$ now let's draw

the phase diagram

So we can see that net amplitude would be zero.