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

Two simple harmonic motions are represented by the equations 
$$y_1=10\sin \left(3\pi t+\dfrac{\pi}{4}\right)$$
and $$y_2=5(3\sin 3\pi t+\sqrt 3 \cos 3\pi t)$$ Their amplitudes are in the ratio of :
  • $$\sqrt 3$$
  • $$1/\sqrt 3$$
  • $$2$$
  • $$1/6$$
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.
  • $$-3.44\ cm+1750\ cm/s, 17\times cm/s^{2}$$
  • $$4.33\ cm+1570\ cm/s,71\times 10^{4}\ cm/s^{2}$$
  • $$-4.33\ cm,+1570\ cm/s,171\times 10^{4}\ cm/s^{2}$$
  • $$-3.44\ cm,-1750\ cm/s,171\times 10^{4}\ cm/s^{2}$$
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 $$120^{\circ}$$. The resultant amplitude will be
  • $$A$$
  • $$2A$$
  • $$4A$$
  • $$\sqrt{2 A}$$
A wave motion has the function $$Y=a_{0}\sin (\omega t-kx)$$. 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 $$x=\pi/2k$$ 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
  • $$12 \,m/s$$
  • $$24 \,m/s$$
  • $$8 \,m/s$$
  • $$16 \,m/s$$
Two coherent waves represented by $$y_1 = A sin \left(\dfrac{2 \pi}{\lambda} x_1 - \omega t + \dfrac{\pi}{6} \right)$$ and $$y_2 = A sin \left(\dfrac{2 \pi}{\lambda} x_2 - \omega t + \dfrac{\pi}{6} \right)$$ are superimposed . The two waves will produce
  • constructive interference at $$(x_1 - x_2) = 2 \lambda$$
  • constructive interference at $$(x_1 - x_2) = 23/24 \lambda$$
  • destructive interference at $$(x_1 - x_2) = 1.5 \lambda$$
  • destructive interference at $$(x_1 - x_2) = 11/24 \lambda$$
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 $$n_1$$ and the other with frequency $$n_2$$. The ratio $$n_1/n_2$$ 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 waves$$y_1 = A_1 sin(\omega t -\beta_1) y_2 = A_2 sin(\omega t - \beta_2)$$ 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 $$y = \dfrac{1}{\sqrt{a}} sin\omega t \pm \dfrac{1}{\sqrt{b}} cos \omega t$$will 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 $$\mu m$$is 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
  • $$\dfrac{6}{5}$$
  • $$\dfrac{2}{3}$$
  • $$\dfrac{1}{7}$$
  • $$\dfrac{5}{9}$$
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