Two simple harmonic motions are represented by equations y 1-4 sin 10 t - and y 2-5 cos 10 t - What is the phase difference between their velocities-A- -B- -2C- -D- -2

Two harmonic waves are represented in SI units by, $y_{1} (x, t) = 0.2 s i n (x - 3.0 t)$ and $y_{2} (x, t) = 0.2 s i n (x - 3.0 t + ϕ)$ . What is the expression for the sum $y = y_{1} + y_{2} f o r ϕ = \frac{π}{2}$ .

Q. Three travelling waves in same direction are superimposed. The equation of wave are

y_{1} = A_{0} s i n (k x - ω t), y_{2} = 3 \sqrt{2} A_{0} s i n (k x - ω t + ϕ)

and

y_{3} = 4 A_{0} c o s (k x - ω t)

. If

0 \leq ϕ \leq π / 2

and the phase difference between resultant wave and first wave is

π / 4

, then

ϕ

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Two simple harmonic motions are represented by equations y1=4sin(10t+ϕ) and y2=5cos(10t). What is the phase difference between their velocities?

The correct option is D (ϕ−π2)Given: y1=4sin(10t+ϕ) y2=5cos(10t) We know that velocity;v=dydt ∴v1=dy1dt=40cos(10t+ϕ) ....(i) v2=dy2dt=−50sin(10t)v2=50cos(10t+π2) ....(ii) From equation (i) and (ii) Phase difference between v1 and v2=|ϕ2−ϕ1| =(π2−ϕ) or (ϕ−π2)

Two simple harmonic motions are represented by equations $y_{1} = 4 sin (10 t + ϕ)$ and $y_{2} = 5 cos (10 t)$ . What is the phase difference between their velocities?