Advertisements
Advertisements
Question
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.
Solution
a, b and d
Explanation:
Given equation is `y(x, t) = 0.06 sin ((2pi)/3 x) cos (120 pit)`
Comparing with standard equation of stationary wave `y(x, t) = a sin(kx) cos(ωt)`
It is represented by the diagram,
Where N denotes nodes and A denotes antinodes.
a. Clearly, frequency is common for all the points.
b. Consider all the particles between two nodes they are having the same phase of (120 πt) at a given time.
c. and d. But are having different amplitudes of `0.06 sin ((2pi)/3 x)` and because of different amplitudes, they are having different energies.
APPEARS IN
RELATED QUESTIONS
An open organ pipe of length L vibrates in its fundamental mode. The pressure variation is maximum
Two wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the second overtone of second wire and radius of first wire is twice the radius of the second then the ratio of length of first wire to second wire is
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.
An organ pipe of length L open at both ends is found to vibrate in its first harmonic when sounded with a tuning fork of 480 Hz. What should be the length of a pipe closed at one end, so that it also vibrates in its first harmonic with the same tuning fork?
The wave pattern on a stretched string is shown in figure. Interpret what kind of wave this is and find its wavelength.
Show that when a string fixed at its two ends vibrates in 1 loop, 2 loops, 3 loops and 4 loops, the frequencies are in the ratio 1:2:3:4.
Two identical strings X and Z made of same material have tension Tx and Tz in them If their fundamental frequencies are 450 Hz and 300 Hz, respectively, then the ratio `"T"_x/"T"_"z"` is ______.
Two travelling waves produce a standing wave represented by the equation. y = 1.0 mm cos (1.57 cm-1) x sin (78.5 s-1)t. The node closest to the origin in the region x > 0 will be at x = ______ cm.
A wire of length 2L is made by joining two wires A and B of the same length but different radii r and 2r, and made of the same material. It is vibrating at a frequency such that the joint of the two wires forms a node. If the number of antinodes in wire A is p and that in B is q then the ratio p : q 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 ______.
