Advertisements
Advertisements
प्रश्न
The wave pattern on a stretched string is shown in figure. Interpret what kind of wave this is and find its wavelength.
Advertisements
उत्तर
All particles are at rest at t = `T/4` and t = `(3T)/4`, which is in the stationary wave when the particle crosses its mean position.
Thus, the graph shows a stationary wave. The wave at x = 10, 20, 30, 40 cm there are nodes and the distance between successive nodes is `λ/2`.
∴ `λ/2 = (30 - 20)`
⇒ λ = 20 cm
APPEARS IN
संबंधित प्रश्न
Explain why (or how) In a sound wave, a displacement node is a pressure antinode and vice versa,
An open organ pipe of length L vibrates in its fundamental mode. The pressure variation is maximum
The number of possible natural oscillations of the air column in a pipe closed at one end of length 85 cm whose frequencies lie below 1250 Hz? (v = 340 m/s)
Water waves produced by a motor boat sailing in water are ______.
The displacement of a string is given by y (x, t) = 0.06 sin (2πx/3) cos (120 πt) where x and y are in m and t in s. The length of the string is 1.5 m and its mass is 3.0 × 10−2 kg.
- It represents a progressive wave of frequency 60 Hz.
- It represents a stationary wave of frequency 60 Hz.
- It is the result of superposition of two waves of wavelength 3 m, frequency 60 Hz each travelling with a speed of 180 m/s in opposite direction.
- Amplitude of this wave is constant.
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.
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 pattern of standing waves formed on a stretched string at two instants of time are shown in figure. The velocity of two waves superimposing to form stationary waves is 360 ms–1 and their frequencies are 256 Hz.
- Calculate the time at which the second curve is plotted.
- Mark nodes and antinodes on the curve.
- Calculate the distance between A′ and C′.
A tuning fork vibrating with a frequency of 512 Hz is kept close to the open end of a tube filled with water (Figure). The water level in the tube is gradually lowered. When the water level is 17 cm below the open end, maximum intensity of sound is heard. If the room temperature is 20°C, calculate
- speed of sound in air at room temperature
- speed of sound in air at 0°C
- if the water in the tube is replaced with mercury, will there be any difference in your observations?
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 ______.
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 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 ______.
A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is ______.
