Question

Two sine waves travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitude of each wave is 4 mm and the phase difference between the waves is 90${}^{\circ }$, what is the resultant amplitude?

• A. 8 mm
• B. $4\sqrt{3}mm$
• C. $2\sqrt{2}mm$
• D. $4\sqrt{2}mm$

Answer 1

The correct option is D $4\sqrt{2}mm$

Giventhe frequency and wavelength of the wave is same, the phase method of calculating resultant amplitude can be used. Here given is that phase difference $\varphi$ is $\frac{\pi }{2}$

Resultant amplitude $A=\sqrt{a_1^2+a_2^2+2a_1{a}_{2}cos\varphi }$

Also$a_1=a_2=4mm$

$A=4\sqrt{2}mm$