Advertisements
Advertisements
प्रश्न
Figure shows a plot of the transverse displacements of the particles of a string at t = 0 through which a travelling wave is passing in the positive x-direction. The wave speed is 20 cm s−1. Find (a) the amplitude, (b) the wavelength, (c) the wave number and (d) the frequency of the wave.
Advertisements
उत्तर
Given:
Wave speed,
ν = 20 cm/s
From the graph, we can infer:
(a) Amplitude, A = 1 mm
(b) Wavelength, λ = 4 cm
(c) Wave number,
\[k = \frac{2\pi}{\lambda}\]
\[= \frac{\left( 2 \times 3 . 14 \right)}{4}\]
\[ = 1 . 57 {cm}^{- 2} \]
(d) Time Period , T = \[\frac{\lambda}{\nu}\]
\[\text{ Frequency, f } = \frac{1}{T} = \frac{v}{\lambda}\]
\[ \Rightarrow f = \frac{20}{4} = 5 Hz\]
APPEARS IN
संबंधित प्रश्न
Explain why (or how) Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases
Explain why (or how) The shape of a pulse gets distorted during propagation in a dispersive medium.
A mechanical wave propagates in a medium along the X-axis. The particles of the medium
(a) must move on the X-axis
(b) must move on the Y-axis
(c) may move on the X-axis
(d) may move on the Y-axis.
A wave moving in a gas
A particle on a stretched string supporting a travelling wave, takes 5⋅0 ms to move from its mean position to the extreme position. The distance between two consecutive particles, which are at their mean positions, is 2⋅0 cm. Find the frequency, the wavelength and the wave speed.
A steel wire of length 64 cm weighs 5 g. If it is stretched by a force of 8 N, what would be the speed of a transverse wave passing on it?
Two wires of different densities but same area of cross section are soldered together at one end and are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.
A transverse wave described by \[y = \left( 0 \cdot 02 m \right) \sin \left( 1 \cdot 0 m^{- 1} \right) x + \left( 30 s^{- 1} \right)t\] propagates on a stretched string having a linear mass density of \[1 \cdot 2 \times {10}^{- 4} kg m^{- 1}\] the tension in the string.
In the arrangement shown in figure , the string has a mass of 4⋅5 g. How much time will it take for a transverse disturbance produced at the floor to reach the pulley? Take g = 10 m s−2.
A heavy but uniform rope of length L is suspended from a ceiling. (a) Write the velocity of a transverse wave travelling on the string as a function of the distance from the lower end. (b) If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceiling? (c) A particle is dropped from the ceiling at the instant the bottom end is given the jerk. Where will the particle meet the pulse?
A transverse wave of amplitude 0⋅50 mm and frequency 100 Hz is produced on a wire stretched to a tension of 100 N. If the wave speed is 100 m s−1, what average power is the source transmitting to the wire?
A 660 Hz tuning fork sets up vibration in a string clamped at both ends. The wave speed for a transverse wave on this string is 220 m s−1 and the string vibrates in three loops. (a) Find the length of the string. (b) If the maximum amplitude of a particle is 0⋅5 cm, write a suitable equation describing the motion.
Three resonant frequencies of a string are 90, 150 and 210 Hz. (a) Find the highest possible fundamental frequency of vibration of this string. (b) Which harmonics of the fundamental are the given frequencies? (c) Which overtones are these frequencies? (d) If the length of the string is 80 cm, what would be the speed of a transverse wave on this string?
The equation of a standing wave, produced on a string fixed at both ends, is
\[y = \left( 0 \cdot 4 cm \right) \sin \left[ \left( 0 \cdot 314 {cm}^{- 1} \right) x \right] \cos \left[ \left( 600\pi s^{- 1} \right) t \right]\]
What could be the smallest length of the string?
