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.
A string is cut into three parts, having fundamental frequencies n1, n2, and n3 respectively. The original fundamental frequency "n" is related by the expression:
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)
Two vibrating tuning forks produce progressive waves given by \(Y_1 = 4 ~\mathrm{sin}~500 \pi \mathrm{t}\) and \(Y_2 = 2 ~\mathrm{sin}~506 \pi \mathrm{t}\). The number of beats produced per minute is:
1. | \(3\) | 2. | \(360\) |
3. | \(180\) | 4. | \(60\) |
If a standing wave having 3 nodes and 2 antinodes is formed within 1.21 Å distance, then the wavelength of the standing wave will be:
1. 1.21 Å
2. 2.42 Å
3. 0.605 Å
4. 4.84 Å
A point source emits sound equally in all directions in a non-absorbing medium.
Two points, P and Q, are at distances of \(2\) m and \(3\) m, respectively, from the source. The ratio of the intensities of the waves at P and Q is:
1. \(3:2\)
2. \(2:3\)
3. \(9:4\)
4. \(4:9\)
A cylindrical tube (L = 125 cm) is resonant with a tuning fork at a frequency of 330 Hz. If it is filled with water, then to get the resonance again, the minimum length of the water column will be:
1. 50 cm
2. 60 cm
3. 25 cm
4. 20 cm
The phase difference between two waves, represented by
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
If a wave is travelling in a positive X-direction with A = 0.2 m, velocity = 360 m/s, and λ = 60 m, then the correct expression for the wave will be:
1. | \(\mathrm{y}=0.2 \sin \left[2 \pi\left(6 \mathrm{t}+\frac{\mathrm{x}}{60}\right)\right]\) |
2. | \(\mathrm{y}=0.2 \sin \left[ \pi\left(6 \mathrm{t}+\frac{\mathrm{x}}{60}\right)\right]\) |
3. | \(\mathrm{y}=0.2 \sin \left[2 \pi\left(6 \mathrm{t}-\frac{\mathrm{x}}{60}\right)\right]\) |
4. | \(\mathrm{y}=0.2 \sin \left[ \pi\left(6 \mathrm{t}-\frac{\mathrm{x}}{60}\right)\right]\) |