The stationary wave y = 2a sinkx cosω t in a stretched string is the result of superposition of y1 = a sin (kx - ω t) and

Question

The stationary wave y = 2a sinkx cosω t in a stretched string is the result of superposition of y1 = a sin (kx - ω t) and (A) y2 = a cos (kx + ω t) (B) y2 = a sin (kx + ω t) (C) y2 = a cos (kx - ω t) (D) y2 = asin (kx - ω t)

Tardigrade Admin · Accepted Answer

y1 = a sin (kx - ω t) y2 = a sin (kx - ω t) According to the principle of superposition, the resultant wave is y = y1 + y2 = a sin(kx - ω t) + a sin(kx + ω t) Using trigonometric identity sin(A + B) + sin(A - B) = 2 sin A cos B we get, y = 2a sin kx cos ω t

Q. The stationary wave $y = 2 a s ink x cos ω t$ in a stretched string is the result of superposition of $y_{1} = a s in (k x - ω t)$ and

$y_{2} = a cos (k x + ω t)$

$y_{2} = a s in (k x + ω t)$

$y_{2} = a cos (k x - ω t)$

$y_{2} = a s in (k x - ω t)$

Q. The stationary wave y=2asinkxcosωt in a stretched string is the result of superposition of y1​=asin(kx−ωt) and

y2​=acos(kx+ωt)

y2​=asin(kx+ωt)

y2​=acos(kx−ωt)

y2​=asin(kx−ωt)

y1​=asin(kx−ωt) y2​=asin(kx−ωt) According to the principle of superposition, the resultant wave is y=y1​+y2​=asin(kx−ωt)+asin(kx+ωt) Using trigonometric identity sin(A+B)+sin(A−B)=2sinAcosB we get, y=2asinkxcosωt

Q. The stationary wave $y = 2 a s ink x cos ω t$ in a stretched string is the result of superposition of $y_{1} = a s in (k x - ω t)$ and

$y_{2} = a cos (k x + ω t)$

$y_{2} = a s in (k x + ω t)$

$y_{2} = a cos (k x - ω t)$

$y_{2} = a s in (k x - ω t)$