Question:
A string of length 0.4 m and mass $10^{-2} kg$ is tightly clamped at its ends. The tensior in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time $\Delta t.$ The minimum value of $\Delta t.$ which allows constructive interference between successive pulses, is
A string of length 0.4 m and mass $10^{-2} kg$ is tightly clamped at its ends. The tensior in the string is 1.6 N. Identical wave pulses are produced at one end at equal intervals of time $\Delta t.$ The minimum value of $\Delta t.$ which allows constructive interference between successive pulses, is
Updated On: Jun 14, 2022
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- 0.10 s
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The Correct Option is B
Solution and Explanation
Mass per unit length of the string.
$\hspace20mm =2.5 \times 10^{-2} kg/m$
$\therefore$ Velocity of wave in the string,
$\hspace15mm v = \sqrt{\frac{T}{m}}=\sqrt{\frac{1.6}{2.5 \times 10^{-2}}}$
$\hspace20mm v = 8\, m/s $
For constructive interference between successive pulses
$\hspace15mm \Delta t_{min} = \frac{2l}{v} $
$\hspace20mm = \frac{(2)(0.4)}{8}=0.10\, s $
(After two reflections, the wave pulse is in same phase as it was produced, since in one reflection its phase changes by $p$, and if at this moment next identical pulse is produced, then constructive interference will be obtained.)
$\hspace20mm =2.5 \times 10^{-2} kg/m$
$\therefore$ Velocity of wave in the string,
$\hspace15mm v = \sqrt{\frac{T}{m}}=\sqrt{\frac{1.6}{2.5 \times 10^{-2}}}$
$\hspace20mm v = 8\, m/s $
For constructive interference between successive pulses
$\hspace15mm \Delta t_{min} = \frac{2l}{v} $
$\hspace20mm = \frac{(2)(0.4)}{8}=0.10\, s $
(After two reflections, the wave pulse is in same phase as it was produced, since in one reflection its phase changes by $p$, and if at this moment next identical pulse is produced, then constructive interference will be obtained.)
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Concepts Used:
Waves
Waves are a disturbance through which the energy travels from one point to another. Most acquainted are surface waves that tour on the water, but sound, mild, and the movement of subatomic particles all exhibit wavelike properties. inside the most effective waves, the disturbance oscillates periodically (see periodic movement) with a set frequency and wavelength.
Types of Waves:
Transverse Waves -
Waves in which the medium moves at right angles to the direction of the wave.
Examples of transverse waves:
- Water waves (ripples of gravity waves, not sound through water)
- Light waves
- S-wave earthquake waves
- Stringed instruments
- Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.
Longitudinal Wave -
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of movement of the wave.
Examples of longitudinal waves:
- Sound waves
- P-type earthquake waves
- Compression wave