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CBSE Questions for Class 11 Engineering Physics Waves Quiz 13 - MCQExams.com

Two simple harmonic motions are represented by the equations 
y1=10sin(3πt+π4)
and y2=5(3sin3πt+3cos3πt) Their amplitudes are in the ratio of :
  • 3
  • 1/3
  • 2
  • 1/6
A simple harmonic wavetrain of amplitude 5 cm and frequency 100 Hz is travelling in the positive x direction with a velocity of 30 m/s. The displacement velocity and acceleration at t=3s of a particle of the medium situated 100 cm from the origin are respectively.
  • 3.44 cm+1750 cm/s,17×cm/s2
  • 4.33 cm+1570 cm/s,71×104 cm/s2
  • 4.33 cm,+1570 cm/s,171×104 cm/s2
  • 3.44 cm,1750 cm/s,171×104 cm/s2
Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120. The resultant amplitude will be
  • A
  • 2A
  • 4A
  • 2A
A wave motion has the function Y=a0sin(ωtkx). The graph in the figure shows how the displacement y at a fixed point varies with time t. Which one of the labeled points shows a displacement equal to that at the position x=π/2k at time t=0
1744937_44570cea597643199f96db02aa1cb15c.png
  • P
  • Q
  • R
  • S
A simple harmonic plane wave propagates along x-axis in a medium. The displacement of the particles as a function of time is shown in figure, for x=0 (curve 1) and x=7 (curve 2).
The two particles are within a span of one wavelength.
The speed of the wave is
1750604_8f81eb770b584271a4f29c1cc9930207.png
  • 12m/s
  • 24m/s
  • 8m/s
  • 16m/s
Two coherent waves represented by y1=Asin(2πλx1ωt+π6) and y2=Asin(2πλx2ωt+π6) are superimposed . The two waves will produce
  • constructive interference at (x1x2)=2λ
  • constructive interference at (x1x2)=23/24λ
  • destructive interference at (x1x2)=1.5λ
  • destructive interference at (x1x2)=11/24λ
Two vibration strings of the same material but lengths L and 2L have radii 2r and r, respectively. The are stretched  under the same tension. Both the strings vibrate in their fundamental modes, the one of length L with frequency n1 and the other with frequency n2. The ratio n1/n2 is given by 
  • 2
  • 4
  • 8
  • 1
Figure 5.55 shows a student setting up wave on a long stretched string. The student's hand makes one complete up and down movement in 0.4 \,s and in each up and down movement the hand moves by a height of 0.3 \,m. The wavelength of the waves on the string is 0.8 \,m.
The amplitude of the wave is
1750513_0896cc1fd009455a8a11f7ac6fe44c79.png
  • 0.15 \,m
  • 0.3 \,m
  • 0.075 \,m
  • cannot be predicted
Four pieces of string each of length L are joined end to end to make a long string of length 4L. The linear mass density of the strings are \mu, 4\mu, 9\mu and 16\mu, respectively. One end of the combined string is tied to a fixed support and a transverse wave has been generated at the other end having frequency f (ignore any reflection and absorptions). String has been stretched under a tension F.
Find the ratio of wavelengths of the waves on four strings, starting from right hand side.
1750426_67e75d4379bc4577bfd93e2d6500dcfd.png
  • 12 : 6 : 4 : 3
  • 4 : 3 : 2 : 1
  • 3 : 4 : 6 : 12
  • 1 : 2 : 3 : 4
Following are equations of four waves:
(i) y_1 = a sin \omega \left(t - \dfrac{x}{v} \right)
(ii) y_2 = a cos \omega \left( t = \dfrac{x}{v} \right)
(iii) z_1 = a sin \omega \left(t - \dfrac{x}{v} \right)
(iv) z_2 = a cos \omega \left( t = \dfrac{x}{v} \right)
Which of the following statements are correct?
  • On superpositin of waves (i) and (iii), a travelling wave having amplitude a\sqrt{2} will be formed
  • Superposition of waves (ii) and (iio) is not possible
  • On superposition of (i) and (ii), a stationary wave having amplitude a\sqrt{2} will be formed
  • On superposition of (iii) and (iv), a transverse stationary wavw will be formed
Two separated sources emit sinusoidal travelling waves but have the same wavelength \lambda  and are in phase at their respective sources. One travels a distance  l_{1}  to get to the observation point while the other travels a distance  l_{2} . The amplitude is minimum at the observation point, if  l_{1}-l_{2}  is an
  • odd integral multiple of \lambda
  • even integral multiple of \lambda
  • odd integral multiple of \lambda / 2
  • odd integral multiple of \lambda / 4
Two waves of nearly same amplitude, same frequency travelling with same velocity are superimposing to give phenomenon of interference, If a_1 and a_2 be their respectively amplitudes, \omega be the frequency for both, v be the velocity for both and \Delta \phi is the phase difference between the two waves then,
  • the resultant intensity varies periodically with time and distance.
  • the resulting intensity with \dfrac{I_min}{I_max} = \left (\dfrac{a_1 - a_2} {a_1 + a_2} \right) ^{2} is obtained
  • both the waves must have been travelling in the same direction and must be coherent.
  • I_B = I_1 + I_2 + 2 \sqrt{I_1 I_2} cos (\Delta \phi), where constructive interference is obtained for path difference that are even multiple of 1/2 \lambda.
n waves are produced on a string in 1 s. When the radius of the string is doubled and the tension is maintained the same, the number of waves produced in 1 s for the same harmonic will be
  • 2n
  • \frac {n} {3}
  • \frac {n} {2}
  • \frac {n} {\sqrt{2}}
One end of a 2.4 m string is held fixed and the other end is attached to a weightless ring that can slide along a frictionless rod as shown in Fig. 7.The three longest possible wavelength for standing waves  in this string are respectively
1751613_6239e4afe84b4dbda5c39522c17d18a2.PNG
  • 4.8 m, 1.6 m and 0.96 m
  • 9.6 m, 3.2 m and 1.92 m
  • 2.4 m, 0.8 m and 0.48 m
  • 1.2 m, 0.4 m and 0.24 m
Which of the following travelling wave will produce standing wave, with nodes at x = 0, when superimposed on y = A \sin{(\omega t - kx)}
  • A \sin{(\omega t + kx)}
  • A \sin{(\omega t + kx + \pi)}
  • A \cos{(\omega t + kx)}
  • A \cos{(\omega t + kx + \pi)}
Microwaves from a transmitter are directed normally towards a plane reflector. A detector moves along the normal to the reflector. Between positions of 14 successive maxima, the detector travels a distance 0.14 m. If the velocity of light is 3 \times 10^{8} m/s, find the frequency of the transmitter.
  • 1.5 \times 10^{10} Hz
  • 10^{10} Hz
  • 3 \times 10^{10} Hz
  • 6 \times 10^{10} Hz
Let the two waves y_1 = A \sin {(kx - \omega t)} and y_2 = A \sin {(kx + \omega t)} form a standing wave on a string. Now if an additional phase difference of \phi is created between two waves, then
  • the standing wave will have a different frequency
  • the standing wave will have a different amplitude for a given point
  • the spacing between two consecutive nodes will change
  • none of the above
Which of the following are transferred from one place to another place by the waves ? 
  • mass
  • wavelength
  • velocity
  • energy
Two waves are given by y_1 = a \sin \left (\omega t - kx \right ) and y_2 = a \cos \left (\omega t - kx \right ). The phase difference between the two waves is
  • \frac{\pi} {4}
  • \pi
  • \frac{\pi} {8}
  • \frac{\pi} {2}
If two waves having amplitudes 2A and A and same frequency andvelocity, propagate in the same direction in the same phase, the resulting amplitude will be
  • 3A
  • \sqrt{5} A
  • \sqrt{2} A
  • A
If amplitude of waves at distance r from a point source is A, the amplitude at a distance 2r will be
  • 2A
  • A
  • A/2
  • A/4
Two waves of same frequency and intensity superimpose with each other in opposite phases, then after superposition the
  • Intensity increases by 4 times
  • Intensity increases by two times
  • Frequency increases by 4 times
  • None of these
Two waves are propagating to the point P along a straight line produced by two sources A and B of simple harmonic and of equal frequency. The amplitude of every wave at P is a and the phase of A is ahead by \dfrac{pi}{3} than that of B and the distance AP is greater than BP by 50 cm. Then the resultant amplitude at the point P will be, if the wavelength is 1 meter

[BVP 2003]
  • 2a
  • \sqrt{3}
  • a\sqrt{2}
  • a
In a plane progressive wave given by y= 25 \cos \left (2\pi t - \pi x \right ), the amplitude and frequency are respectively                              [BCECE 2003]

  • 25, 100
  • 25, 1
  • 25, 2
  • 50 \pi, 2
A simple harmonic progressive wave is represented by the equation : y = 8 \sin 2 \pi \left (0.1x - 2t  \right ) where x and y are in cm and t is in seconds. At any instant the phase difference between two particles separated by 2.0 cm in the x-direction is     [MP PMT 2000]
  • 18
  • 36
  • 54
  • 72
The displacement of the interfering light waves are y_1 = 4 sin\omega t and y_2=3 sin \left(\omega t + \dfrac{\pi}{2}\right) . What is the amplitude of the resultant wave
  • 5
  • 7
  • 1
  • 0
A transverse progressive wave on a stretched string has a velocity of 10ms^{-1} and a frequency of 100 Hz. The phase difference between two particles of the string which are 23 cm apart will be
  • \frac{\pi} {8}
  • \frac{\pi} {4}
  • \frac{3\pi} {8}
  • \frac{\pi} {2}
Two waves of frequencies 20 Hz and 30 Hz. Travels out from a common point. The phase difference between them after 0.6 sec is
  • 12\pi
  • \dfrac{\pi} {2}
  • \pi
  • \dfrac{3\pi} {4}
Two wavesy_1 = A_1 sin(\omega t -\beta_1) y_2 = A_2 sin(\omega t - \beta_2) Superimpose to form a resultant wave whose amplitude is [CPMT 1999]
  • \sqrt{A_1^2 + A_2^2 +2A_1A_2cos(\beta_1 - \beta_2) }
  • \sqrt{A_1^2 + A_2^2 +2A_1A_2sin(\beta_1 - \beta_2) }
  • A_1 + A_2
  • | A_1 + A_2 |
The amplitude of a wave represented by displacement equation y = \dfrac{1}{\sqrt{a}} sin\omega t \pm \dfrac{1}{\sqrt{b}} cos \omega twill be

  • \dfrac{a+b}{ab}
  • \dfrac{\sqrt{a}+{b}}{ab}
  • \dfrac{\sqrt{a}\pm\sqrt{b}}{ab}
  • \sqrt{\dfrac{a+b}{ab}}
The path difference between the two waves y_1 = a_1 \sin \left (\omega t - \frac{2 \pi x} {\lambda}  \right ) and y_2 = a_2 \cos \left (\omega t - \frac{2 \pi x} {\lambda} + \phi \right )            [MP PMT 1994]
  • \frac{\lambda} {2 \pi} \phi
  • \frac{\lambda} {2 \pi} \left (\phi + \frac{\pi} {2} \right )
  • \frac {2 \pi} {\lambda} \left (\phi - \frac{\pi} {2} \right )
  • \frac {2 \pi} {\lambda}\phi
Two waves are represented by y_1 = a sin \left(\omega t +\dfrac{\pi}{6}\right)and y_2 = a cos \omega t What will be their resultant amplitude

  • a
  • \sqrt{2}a
  • \sqrt{3} a
  • 2 a
The phase difference between two points separated by 0.8 m in a wave of frequency 120 Hz is 90^{0}. Then the velocity of wave will be
  • 192 m/s
  • 360 m/s
  • 710 m/s
  • 384 m/s
The phase difference between two waves represented by y_1 = 10^{-6} \sin \left [100 t + (x/50) + 0.5  \right ] m, y_2 = 10^{-6} \cos \left [100 t + (x/50) \right ] m where x is expressed in meters and t is expressed in seconds, is approximately         [CBSE PMT 2004]
  • 1.5 rad
  • 1.07 rad
  • 2.07 rad
  • 0.6 rad
A man x can hear only upto 10 kHz and another man y upto 20 Hz. A note of frequency 500 Hz is produced before them from a stretched string. Then
  • Both will hear sounds of same pitch but different quality
  • Both will hear sounds of different pitch but same quality
  • Both will hear sounds of different pitch and different quality
  • Both will hear sounds of same pitch and same quality
The phase difference between the two particles situated on both the side of a node is

  • 0^\cdot
  • 90^\cdot
  • 180^\cdot
  • 360^\cdot
The equation y = A cos^2 \left(2\pi n t - 2\pi \dfrac{x}{\lambda}\right) represents a wave with
  • Amplitude A/2, frequency 2n and wavelength \lambda / 2
  • Amplitude A/2, frequency 2n and wavelength \lambda
  • Amplitude A, frequency 2n and wavelength 2\lambda
  • Amplitude A, frequency n and wavelength \lambda
Three waves of equal frequency having amplitudes 10 \mu m, 4 \mu m and 7 \mu m  arrive at a given point with successive phase difference of \dfrac{\pi}{2} The amplitude of the resulting wave in \mu mis given by 
  • 7
  • 6
  • 5
  • 4
Two waves having sinusoidal waveforms have different wavelengths and different amplitude. They will be having
  • Same pitch and different intensity
  • Same quality and different intensity
  • Different quality and different intensity
  • Same quality and different pitch
In a wave, the path difference corresponding to a phase difference of \phi is
  • \dfrac{\pi}{2 \lambda} \phi
  • \dfrac{\pi}{ \lambda} \phi
  • \dfrac{\lambda}{2\pi} \phi
  • \dfrac{\lambda}{\pi} \phi
Equation of motion in the same direction are given by 
y_1 = 2a \sin \left (\omega t - kx  \right ) and y_1 = 2a \sin \left (\omega t - kx - \theta \right )
The amplitude of the medium particle will be    [CPMT 2004]
  • 2a \cos \theta
  • \sqrt{2}a \cos \theta
  • 2a \cos \theta/2
  • \sqrt{2}a \cos \theta/2
Given in the graph above, the points A, B, C, D represents state of vibration of a sound wave. From the below-mentioned options which represent the wavelength.

1849773_76806da9c6c542f2ae7c778745dd5064.png
  • Distance between A and C.
  • Distance between A and D.
  • Distance between A and B.
  • Distance between B and C.
Light travels in the form of
  • Waves
  • Packets
  • Straight Lines
  • None of these
A certain transverse sinusoidal wave of wavelength 20 cm is moving in the positive x direction. The transverse velocity of the particle at x = 0 as a function of time is shown. The amplitude of the motion is :
72094.png
  • \dfrac{5}{\pi} cm
  • \dfrac{\pi}{2}cm
  • \dfrac{10}{\pi}cm 
  • 2\pi cm
A wave of frequency 500 Hz has a phase velocity of 360 m/s. The phase difference between the two displacements at a certain point in a time interval of 10^{-3} seconds will be how much?
  • \displaystyle \frac{\pi}{2} radian
  • \pi radian
  • \displaystyle \frac{\pi}{4} radian
  • \displaystyle \frac{\pi}{8} radian
Find the size of object which can be featured with 5\space MHz in water.
  • 0.148 mm
  • 0.3 mm
  • 0.5 mm
  • 0.1 mm
The frequency of fork is 512 Hz and the sound produced by it travels 42 metres as the tuning fork completes 64 vibrations. Find the velocity of sound :
  • 336 m/sec
  • 320 m/sec
  • 340 m/sec
  • 350 m/sec
A particle is executing SHM of amplitude A, about the mean position x=0. Which of the following is a possible phase difference between the positions of the particle at x=+\dfrac{A}{2} and x=-\dfrac{A}{\sqrt{2}}.
  • {75^{\circ}}
  • {165^{\circ}}
  • {135^{\circ}}
  • {195^{\circ}}
The theory that can explain the phenomenon of interference, diffraction and polarisation is
  • Wave Theory
  • Plank's Theory
  • Wave theory of Light
  • None of these
Travelling wave travels in medium '1' and enters into another medium '2' in which it's speed gets decreased to 25\%. Then magnitude of ratio of amplitude of transmitted to reflected wave is
  • \dfrac{6}{5}
  • \dfrac{2}{3}
  • \dfrac{1}{7}
  • \dfrac{5}{9}
0:0:1


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