Advertisements
Advertisements
प्रश्न
Which of the following statements are true for a stationary wave?
- Every particle has a fixed amplitude which is different from the amplitude of its nearest particle.
- All the particles cross their mean position at the same time.
- All the particles are oscillating with same amplitude.
- There is no net transfer of energy across any plane.
- There are some particles which are always at rest.
उत्तर
a, b, d and e
Explanation:
We know that the standard equation of stationary wave is
`y(x, t) = 2a sin (kx) cos (ωt)`
In stationary waves, the particles between the two nodes vibrate with different amplitudes. The amplitude increases from node to antinodes from zero to maximum and then from antinodes to nodes amplitude decreases from maximum to zero. The amplitude of a particle will remain constant, but the amplitude will vary with λ.
∴ `k = (2π)/λ`. This verifies option (a) and rejects option (c).
The particles present at nodes have amplitude zero. Hence, verifies option (e).
We know that particles at nodes are at rest. Therefore, there is no energy transfer. This verifies option (d).
Particles between the two nodes are in the same phase, it means the motion of particles will be either upward or downward. Thus, particles will cross the mean position at the same time. This verifies option (b).
APPEARS IN
संबंधित प्रश्न
Explain why (or how) In a sound wave, a displacement node is a pressure antinode and vice versa,
A bat is flitting about in a cave, navigating via ultrasonic beeps. Assume that the sound emission frequency of the bat is 40 kHz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.03 times the speed of sound in air. What frequency does the bat hear reflected off the wall?
An open organ pipe of length L vibrates in its fundamental mode. The pressure variation is maximum
Two wires are kept tight between the same pair of supports. The tensions in the wires are in the ratio 2 : 1 the radii are in the ratio 3 : 1 and the densities are in the ratio 1 : 2. Find the ratio of their fundamental frequencies.
A 2 m long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200 m s−1 and the amplitude is 0⋅5 cm. (a) Find the wavelength and the frequency. (b) Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x = 50 cm has reached its maximum displacement.
The transverse displacement of a string (clamped at its both ends) is given by y(x, t) = 0.06 sin (2πx/3) cos (120 πt). All the points on the string between two consecutive nodes vibrate with ______.
- same frequency
- same phase
- same energy
- different amplitude.
A sonometer wire is vibrating in resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be is resonance with the wire?
The wave pattern on a stretched string is shown in figure. Interpret what kind of wave this is and find its wavelength.
Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass 'm' and has another weight of mass 2m hung at a distance of 75 cm from A. The tension in the string at A is :
Two closed end pipes when sounded together produce 5 beat per second. If their length are in the ratio 100 : 101, then fundamental notes produced by them are ______.
