Question 56: Waves

Question

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.

Accepted Answer

$A_{R}=\sqrt{A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2} \cos \phi}$
$$
\begin{aligned}
& 8=\sqrt{8^{2}+8^{2}+2 	imes 8 	imes 8 \cos \phi} \\
& \Rightarrow \cos \phi=-\frac{1}{2} \\
& \Rightarrow \phi=120^{\circ}
\end{aligned}
$$

Waves

Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.

Integer / Numeric Answer Type