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Wave Motion and Waves on a String Physics - Wave Motion and Waves on a String

Rajasthan Board (RBSE) - STD 12 Science - Physics (Rajasthan - English Medium). 77 questions in this chapter.

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Wave Motion and Waves on a String question types

77 questions across 5 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

77
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5
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5
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Sample Questions

Wave Motion and Waves on a String questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
A wave pulse, travelling on a two -piece string, gets partially reflected and partially transmitted at the junction. The reflected wave is inverted in shape as compared to the incident one. If the incident wave has wavelengt $\lambda$ and the transmitted wave $\lambda'.$
  • A
    $\lambda'>\lambda$
  • B
    $\lambda'=\lambda$
  • ✓
    $\lambda'<\lambda$
  • D
    Nothing can be said about the relation of $\lambda$ and $\lambda'.$

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
Consider two waves passing through the same string. Principle of superposition for displacement says that the net displacement of a particle on the string is sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for:
  • A
    Both the velocity and the kinetic energy.
  • ✓
    The velocity but not for the kinetic energy.
  • C
    The kinetic energy but not for the velocity.
  • D
    Neither the velocity nor the kinetic energy.

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
A wave is represented by the equation $-\text{y}=(0.001\text{mm})\sin\Big[(50\text{s}^{-1})\text{t}+(2.0\text{m}^{-1})\text{x}\Big]$
  1. The wave velocity $= 100m/s.$
  2. The wavelength $= 2.0m.$
  3. The frequency $=\frac{25}{\pi}\text{Hz}$
  4. The amplitude $= 0.001mm.$
  • A
    $a$ and $ b$
  • B
    $a$ and $c$
  • C
    $c$ and $d$ 
  • D
    $b$ and $d$
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Q 71 Marks Question1 Mark
A string clamped at both ends vibrates in its fundamental mode. Is there any position (except the ends) on the string which can be touched without disturbing the motion? What if the string vibrates in its first overtone?
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Q 91 Marks Question1 Mark
Show that for a wave travelling on a string:$\frac{\text{y}_\text{max}}{\text{u}_\text{max}}=\frac{\text{v}_\text{max}}{\text{a}_\text{max}},$
Where the symbols have usual meanings. Can we use componendo and dividendo taught in algebra to write,$\frac{\text{y}_\text{max}+\text{v}_\text{max}}{\text{y}_\text{max}-\text{v}_\text{max}}=\frac{\text{v}_\text{max}+\text{a}_\text{max}}{\text{v}_\text{max}-\text{a}_\text{max}}?$
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Q 101 Marks Question1 Mark
A wave pulse passing on a string with a speed of 40cm/s in the negative x-direction has its maximum at x = 0 at t = 0. Where will this maximum be located at t = 5s?
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Q 113 Marks Question3 Marks
A steel wire of mass 4.0g and length 80cm is fixed at the two ends. The tension in the wire is 50N. Find the frequency and wavelength of the fourth harmonic of the fundamental.
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Q 123 Marks Question3 Marks
The equation of a wave travelling on a string is:$\text{y}=(0.10\text{mm})\sin\big[(31.4\text{m}^{-1})\text{x}+(314\text{s}^{-1})\text{t}\big].$
  1. In which direction does the wave travel?
  2. Find the wave speed, the wavelength and the frequency of the wave.
  3. What is the maximum displacement and the maximum speed of a portion of the string?
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Q 133 Marks Question3 Marks
Figure, shows a string stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a particular tuning fork. When a beaker containing water is brought under the block so that the block is completely dipped into the beaker, the string vibrates in its eleventh harmonic. Find the density of the material of the block.
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Q 143 Marks Question3 Marks
Figure, shows an aluminium wire of length 60cm joined to a steel wire of length 80cm and stretched between two fixed supports. The tension produced is 40N. The cross-sectional area of the steel wire is $1.0mm^2$ and that of the aluminium wire is $3.0 mm^2$. What could be the minimum frequency of a tuning fork which can produce standing waves in the system with the joint as a node? The density of aluminium is $2.6g/cm^3$ and that of steel is $7.8g/cm^3.$​​​​​​​
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Q 153 Marks Question3 Marks
Two wires of different densities but same area of crosssection 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.
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Q 165 Marks Questions5 Marks
A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at t = to is given by $\text{g}(\text{x},\text{t}_0)=\text{A}\sin\big(\frac{\text{x}}{\text{a}}\big).$ Write the wave equation for a general time t.
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Q 175 Marks Questions5 Marks
A uniform horizontal rod of length 40cm and mass 1.2kg is supported by two identical wires as shown in figure, Where should a mass of 4.8kg be placed on the rod so that the same tuning fork may excite the wire on left into its fundamental vibrations and that on right into its first overtone? Take $g = 10m/s^2.$
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Q 185 Marks Questions5 Marks
A wave travels along the positive x-direction with a speed of 20m/s. The amplitude of the wave is 0.20cm and the wavelength 2.0cm.
  1. Write a suitable wave equation which describes this wave.
  2. What is the displacement and velocity of the particle at x = 2.0cm at time t = 0 according to the wave equation written? Can you get different values of this quantity if the wave equation is written in a different fashion?
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Q 195 Marks Questions5 Marks
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.
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Q 205 Marks Questions5 Marks
A heavy but uniform rope of length L is suspended from a ceiling.
  1. Write the velocity of a transverse wave travelling on the string as a function of the distance from the lower.
  2. If the rope is given a sudden sideways jerk at the bottom, how long will it take for the pulse to reach the ceiling?
  3. A particle is dropped from the ceiling at the instant the bottom end is given the jerk. Where will the particle meet the pulse ?
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Q 22Case study (4 Marks)4 Marks
A 4.0kg block is suspended from the ceiling of an elevator through a, string having a linear mass density of $19.2 \times 10^{-3}kg/m.$ Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of $2.0m/s^2.$ Take $g = 10m/s^2.$
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