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?

8 mm

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Solution

The correct option is D

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 $ϕ$ is $\frac{π}{2}$

Resultant amplitude $A = \sqrt{a_{1}^{2} + a_{2}^{2} + 2 a_{1} a_{2} c o s ϕ}$

Also $a_{1} = a_{2} = 4 m m$

$A = 4 \sqrt{2} m m$

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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∘, what is the resultant amplitude?

The correct option is D 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 ϕ is π2 Resultant amplitude A=√a21+a22+2a1a2cosϕ Alsoa1=a2=4mm A=4√2mm

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?