Question

Two waves, each having a frequency of $100Hz$ and a wavelength of $2.0cm$, are travelling in the same direction on a string. What is the phase difference between the waves if the second wave was produced $0.015s$, later than the first one at the same place.

Answer 1

Step 1: Given

Frequency: $f=100Hz$

Wavelength: $\lambda =2cm=2\times {10}^{-2}m$

Step 2: Formula Used

$\varphi =\frac{2\mathrm{\pi x}}{\lambda }$

Step 3: Find the path difference

Calculate the wave speed by multiplying the frequency and wavelength.

$$\begin{gathered} v=f\lambda \\ =100\times 2\times {10}^{-2} \\ =2m/s \end{gathered}$$

Calculate the path difference (x) between two waves

$$\begin{gathered} x=vt \\ =2m/s\times 0.015s \\ =0.03m \end{gathered}$$

Step 4: Calculate the phase difference using the formula

$$\begin{gathered} \varphi =\frac{2\mathrm{\pi x}}{\lambda } \\ =\frac{2\pi \times 0.03}{2\times {10}^{-2}} \\ =3\mathrm{\pi } \end{gathered}$$

Hence, the phase difference is $3\mathrm{\pi }$.