The transverse displacement y(x,t) of a wave on a string is give

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 Multiple Choice QuestionsMultiple Choice Questions

1.

Match List-I (Electromagnetic wave type) with List-II (Its association/application) and select the correct option from the choices given below the lists:

  List I   List II
A. Infared waves 1. To treat muscular strain
B. Radio waves 2. For broadcasting
C. X -rays 3. To detect fracture of bones
D. Ultraviolet 4. Absorbed by the ozone layer of the atmosphere

  • A B C D
    4 3 2 1
  • A B C D
    1 2 4 3
  • A B C D
    3 2 1 4
  • A B C D
    3 2 1 4
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2.

The transverse displacement y(x,t) of a wave on a string is given by
straight y left parenthesis straight x comma straight t right parenthesis space equals space straight e to the power of negative left parenthesis ax squared plus bt squared space plus space 2 square root of ab space xt right parenthesis end exponent
This represents a

  • wave moving in +x direction with speed square root of straight a over straight b end root

  • wave moving in -x direction with speed square root of b over a end root

  • standing wave frequency square root of straight a

  • standing wave frequency square root of straight a


B.

wave moving in -x direction with speed square root of b over a end root

Given wave is,
straight y space left parenthesis straight x comma straight t right parenthesis space equals space straight e to the power of negative left parenthesis ax squared space plus bt squared space plus 2 square root of ab space xt right parenthesis end exponent
space equals space straight e to the power of negative left parenthesis square root of ax space plus square root of bt right parenthesis squared end exponent
It space is space straight a space function space of space type space straight y space equals space straight f left parenthesis ωt space plus kx right parenthesis
space equals space straight f open parentheses straight t minus straight x over straight v close parentheses
Where space straight v space is space the space wave space velocity.
therefore space straight y space left parenthesis straight x comma straight t right parenthesis space represents space wave space travelling space along space minus straight x space direction
Speed space of space wave space space equals space straight omega over straight k space equals space fraction numerator square root of straight b over denominator square root of straight a end fraction space equals space square root of straight b over straight a end root

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3.

In amplitude modulation, sinusoidal carrier frequency used is denoted by ωc and the signal frequency is denoted by ωm. The bandwidth (Δωm) of the signal is such that Δωm << ωc. Which of the following frequencies is not contained in the modulated wave?

  • ωm + ωc

  • ωc - ωm

  • ωm

  • ωm

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4.

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer?
(speed of light = 3 × 108 ms–1)

  • 17.3 GHz

  • 15.3 GHz

  • 10.1 GHz

  • 10.1 GHz

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5.

Three sound waves of equal amplitudes have frequencies (ν – 1), ν, (ν + 1). They superpose to give beats. The number of beats produced per second will be.

  • 4

  • 3

  • 2

  • 2

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6.

A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 cos (αx −βt). If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then α and β in appropriate units are 

  • α = 25.00 π, β = π

  • α = 0.08/ π,  2.0/π

  • α = 0.04 / π , β =1.0/π

  • α = 0.04 / π , β =1.0/π

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7.

A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed v ms−1. The velocity of sound in air is 300 ms−1. If the person can hear frequencies upto a maximum of 10,000 Hz, the maximum value of v upto which he can hear the whistle is

  • 15 square root of 2 space ms to the power of negative 1 end exponent
  • 15 divided by square root of 2 space ms to the power of negative 1 end exponent
  • 15 ms-1

  • 15 ms-1

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8.

When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per seconds are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2?

  • 200 Hz

  • 202 Hz

  • 196 Hz

  • 196 Hz

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9.

An observer moves towards a stationary source of the sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

  • 0

  • 0.5%

  • 5%

  • 5%

496 Views

10.

The displacement y of a particle in a medium can be expressed as y = 10−6 sin(110t + 20 x + π/4) m, where t is in seconds and x in a meter. The speed of the wave is

  • 2000 m/s

  • 5 m/s

  • 20 m/s

  • 20 m/s

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