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Two waves are simultaneously passing through a string. The equations of the waves are given by
y₁ = A₁ sin k(x − vt) and y₂ = A₂sin k(x − vt + x₀),
where the wave number k = 6.28 cm⁻¹ and x₀ = 1.50 cm. The amplitudes are A₁ = 5.0 mm and A₂ = 4.0mm. Find the phase difference between the waves and the amplitude of the resulting wave

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An Intiative by Sri Chaitanya

δ = 1.5 π and amplitude = 2.00 mm

δ = 2.5 π and amplitude = 1.5 mm

δ = 2.5 π and amplitude = 1.00 mm

δ = 3 π and amplitude = 1.00 mm

answer is D.

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Detailed Solution

The phase of the first wave is k (x − vt) and the second is k (x − vt + x₀).

The phase difference is,

therefore,
δ = k x₀ = (6.28/cm ) (1.50 cm) = 2 π × 1.5 = 3 π.

The waves satisfy the condition of destructive interference.

The amplitude of the resulting wave is given by |A₁ − A₂|

= 5.0 mm − 4.0 mm = 1.0 mm

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