If the two waves represented by y1 = 4 sinω t m and y2 = 3sin(ω t + π/3) m interfere at a point, the amplitude of the resulting wave will be about

Question

If the two waves represented by y1 = 4 sinω t m and y2 = 3sin(ω t + π/3) m interfere at a point, the amplitude of the resulting wave will be about (A) 7 m (B) 5 m (C) 6 m (D) 3.5 m

Tardigrade Admin · Accepted Answer

y1=4sinω t y2=3sin(ω t+π/3) Here, a=4 m, b=3 m, φ=π/3 R=√a2+b2+2ab cos φ =√42+32+2ab cos φ =√42+32+2×4×3 cos π/3 =√37≈6 m

Q. If the two waves represented by $y_{1} = 4 s inω t m$ and $y_{2} = 3 s in (ω t + π /3) m$ interfere at a point, the amplitude of the resulting wave will be about

$7 m$

$5 m$

$6 m$

$3.5 m$

$y_{1} = 4 s inω t$
$y_{2} = 3 s in (ω t + π /3)$
Here, $a = 4 m$ , $b = 3 m$ , $ϕ = π /3$
$R = a^{2} + b^{2} + 2 ab cos ϕ$
$= 4^{2} + 3^{2} + 2 ab cos ϕ$
$= 4^{2} + 3^{2} + 2 \times 4 \times 3 cos π /3$
$= 37 \approx 6 m$

Q. If the two waves represented by y1​=4sinωtm and y2​=3sin(ωt+π/3)m interfere at a point, the amplitude of the resulting wave will be about

7m

5m

6m

3.5m