For a wave \(y=y_0 \sin (\omega t-k x)\), for what value of \(\lambda\) is the maximum particle velocity equal to two times the wave velocity?
1. \(\pi y_0\)
2. \(2\pi y_0\)
3. \(\pi y_0/2\)
4. \(4\pi y_0\)
Two stationary sources exist, each emitting waves of wavelength λ. If an observer moves from one source to the other with velocity u, then the number of beats heard by him is equal to:
1.
2.
3.
4.
The equations of two waves are given as x = acos(ωt + δ) and y = a cos (ωt + ), where δ = + /2, then the resultant wave can be represented by:
1. a circle (c.w)
2. a circle (a.c.w)
3. an ellipse (c.w)
4. an ellipse (a.c.w)
1. | \(3\) | 2. | \(360\) |
3. | \(180\) | 4. | \(60\) |
1. | \(50~\text{cm}\) | 2. | \(60~\text{cm}\) |
3. | \(25~\text{cm}\) | 4. | \(20~\text{cm}\) |
The phase difference between two waves, represented by
\(y_1= 10^{-6}\sin \left\{100t+\left(\frac{x}{50}\right) +0.5\right\}~\text{m}\)
\(y_2= 10^{-6}\cos \left\{100t+\left(\frac{x}{50}\right) \right\}~\text{m}\)
where \(x\) is expressed in metres and \(t\) is expressed in seconds, is approximate:
1. \(2.07\) radians
2. \(0.5\) radians
3. \(1.5\) radians
4. \(1.07\) radians
1. | \({y}=0.2 \sin \left[2 \pi\left(6{t}+\frac{x}{60}\right)\right]\) |
2. | \({y}=0.2 \sin \left[ \pi\left(6{t}+\frac{x}{60}\right)\right]\) |
3. | \({y}=0.2 \sin \left[2 \pi\left(6{t}-\frac{x}{60}\right)\right]\) |
4. | \(y=0.2 \sin \left[ \pi\left(6{t}-\frac{x}{60}\right)\right]\) |