Question 1 : A wave is travelling on a string with the frequency $4$ cycles per second, and its speed is 0.08 meters per second.<br/>Calculate the time period of the wave?

Question 2 : Identify which of the properties is equal to the reciprocal of the Time period?<br/>I. Speed<br/>II. Wavelength<br/>III. Frequency<br/>

Question 3 : The periodic time of a vibrating body is 0.01 sec. Its frequency will be

Question 4 : The height of the crests of a wave is called its :

Question 5 : A radio station transmits waves of wavelength 400 m. If the speed of the waves is $4\, \times\, 10^8\, ms^{-1}$, Find the frequency of the radio station.

Question 7 : Water waves are both longitudinal and transverse. State whether true or false

Question 8 : A longitudinal wave is represented by $x=x_0\,sin\,2\pi(nt-\dfrac{\pi}{\lambda})$. The maximum particle velocity will be four times the wave velocity if

Question 9 : The transverse displacement y(x,t) of a wave on a string is given by y(x,t) = ${ e }^{ \left( { ax }^{ 2 }+{ bt }^{ 2 }+2\sqrt { ab } xt \right) }$.This represents a<br><br>

Question 10 : Identify the parameter which measures the time it takes to complete one cycle?<br/>

Question 11 : A film of oil on a puddle in a parking lot shows a variety of bright colors in swirled patches. What can you say about the thickness of the oil film?

Question 12 : The maximum velocity of a body undergoing S.H.M. is $0.2 m/s$ and its acceleration at $0.1 m$ from the mean position is $0.4 m/s^{-2}$ The amplitude of the S.H.M. is:

Question 14 : What is the wave number of a beam of light in air if its frequency is $14\times 10^{14}$ Hz.

Question 15 : Air column of 20 cm length in a resonance tube resonates with a certain tuning fork when sounded&#160;at its upper open end. The lower end of the tube is closed and adjustable by changing the quantity &#160;of mercury filled inside the tube. The temperature&#160;of the air is 27$^{o}$C. The change in length of the air&#160;column required, if the temperature falls to 7$^{o}$C&#160;and the same tuning fork is again sounded at the&#160;upper open end is &#160;<br/>

Question 16 : Two coherent waves are represented by&#160;$y_{1} =a_{1} &#160;\cos &#160; \omega&#160; t$&#160; and $y_{2} =a_{2} \sin &#160; \omega&#160; t$. The resultant&#160;intensity due to interference will be<br/>

Question 17 : A closed organ pipe (closed at one end) is excited so as to support the third overtone. It is then found that in the pipe, there are:

Question 18 : The path difference between the two waves<br/><br/>$y_{1}=a_{1}\displaystyle \sin(\omega t-\dfrac{2\pi \mathrm{x}}{\lambda})$ and <br/>$y_{2}=a_{2}\displaystyle \cos( \omega t-\dfrac{2\pi\mathrm{x}}{\lambda}+\theta)$ &#160; is<br/>

Question 19 : In a ripple tank when one pulse is sent every tenth of a second , the distance between consecutive pulses is $30 mm$. In the same depth of water pulses are produced at half second intervals. What is the new distance between consecutive pulses ?

Question 20 : In sine waves minimum distance between 2 particles always having same speed is

Question 21 : A long string having a cross-sectional area $0.80 mm^2$&#160;mm2and density, $12.5 g/cc$ is subjected to a tension of $64 N$ along the positive x-axis. One end of this string is attached to a vibrator at $x = 0$ moving in transverse direction at a frequency of $20 Hz$. At $t = 0$, the source is at a maximum displacement $y = 1.0 cm.$&#160;What is the displacement of the particle of the string at $x = 50 cm$ at time $t = 0.05 s$ ?

Question 22 : Assertion: Ratio of maximum intensity and minimum intensity in interference is 25 : 1. Hence amplitude ratio of two waves should be 3 : 2. Reason: $\displaystyle \frac{I_{max}}{I_{min}}\, =\, \left (\displaystyle \frac{A_1\, +\, A_2}{A_1\, -\, A_2}\right )^2$

Question 23 : A uniform string fixed at both ends is vibrating in 3rd harmonic and equation $y = 4 ( \mathrm { cm } )$ $\sin \left[ \left( 0.8 \mathrm { cm } ^ { - 1 } \right) \times \right] \cos \left[ \left( 400 \pi \mathrm { s } ^ { - 1 } \right) t \right]$The length of the vibrating string is<br/>

Question 24 : The equation of a travelling wave is given as $y=5\sin 10\pi (t-0.01\ x)$, along the $x-$ axis. Here all quantities are in $SI$ units. The phase difference between the points separated by a distance of $10\ m$ along $x-$ axis is:

Question 25 : The displacement $y$ in centimeters is given in terms of time $t$ in second by the equation: $y=3\sin 3.14t+4\cos 3.14 t$, then the amplitude of SHM is<br/>

Question 26 : For a longitudinal sound wave, ($B$ is the engineering modulus of the medium and $\rho$ is the density):<br/>

Question 27 : State whether true or false:<br/>Speed of sound can never exceed the average molecular speed in a fluid.&#160;<br/>

Question 28 : The waves are represented by the following equations <br>$y_{1} = 5 \sin 2 \pi (10t-0.1x)$ <br>$y_2 = 10 \sin 2\pi (20t-0.2x)$ <br>Ratio of intensities $\dfrac {I_{2} }{I_{1}}$ will be :<br>

Question 29 : State whether true or false :<br>During constructive interference, the crest of one wave meets the crest of the other wave or the trough of one wave meets the trough of the other wave.

Question 30 : $y_1 = 88\, sin(\omega t - kx)$ and $y_2 = 6 sin(\omega t + kx)$ are two waves travelling in a string of area of cross-section $s$ and density $\rho$. These two waves are superimposed to produce a standing wave.&#160;Find the total amount of energy crossing through a node per second.

Question 31 : Two simple harmonic motions are represented by<br>${ y }_{ 1 }=5\left( \sin { 2\pi t } +\sqrt { 3 } \cos { 2\pi t } \right) $<br>${ y }_{ 2 }=5\left( \sin { 2\pi t } +\cfrac { \pi }{ 4 } \right) $<br>The ratio of the amplitude of two S.H.M's is

Question 32 : The velocity and amplitude of the component traveling waves are respectively<br/>

Question 33 : A wave travelling along positive x-axis is given by $=A\sin { \left( \omega t-kx \right) } $. If it is reflected from a rigid boundary such that $80$% amplitude is reflected, then equation of reflected wave is

Question 35 : A cylindrical block of density $\rho&#160;$ is partially immersed in a liquid of density $3\ \rho$. The plane surface of the block remains parallel to the surface of the liquid. The height of the block is $60\ cm$. The block performs SHM when displaced from its mean position. [Use $g = 9.8 m/s^{2}$]

Question 36 : Equations of a stationary wave and a travelling wave are ${ y }_{ 1 } = a\ sinkx\ cos \omega t$ and ${ y }_{ 2 } = a\ sin (\omega t - kx)$. The phase difference between two points ${ x }_{ 1 }\ =\ \dfrac { \pi }{ 3k } \ and\ { x }_{ 2 }\ =\ \dfrac { 3\pi }{ 2k } \ is\ { \phi }_{ 1 }$ for the first wave and ${ \phi }_{ 2 }$ for the second wave. The ratio $\dfrac { { \phi }_{ 1 } }{ { \phi }_{ 2 } }$ is :

Question 37 : Select correct statement regarding waves on a string [all symbols have their usual meanings].<br/>

Question 38 : A transverse sinusoidal wave is generated at one end of a long horizontal string by a bar that moves the end&#160;up and down through a distance by $2.0 cm.$ The motion of bar is continuous and is repeated regularly $125$&#160;times per sec. If the distance between adjacent wave crests is observed to be $15.7 cm$ and the wave is&#160;moving along +ve x-direction, and at $t = 0$ ,&#160;the element of the string at $x = 0$ &#160; is&#160;&#160; at&#160;&#160; mean &#160; position $y = 0 $&#160;and is moving downwards, the equation of the wave is best described by :&#160;$ (use \pi = 3.14)$<br/>

Question 39 : A wave $10\sin{(ax+bt)}$ is reflected from dense medium at an origin. If 81% of energy is reflected then the equation of reflected wave is

Question 40 : When stationary waves are produced in a medium, which physical characteristic change at antinodes?<br/><br/>

Question 41 : The equation of the wave starting from $x=2\ at\ t=1s$ travelling along negative X-axis&#160;is given by<br/>

Question 42 : Two radio stations broadcast their programmes at the same amplitude $\displaystyle A$ and at slightly different frequencies $\displaystyle \omega_1$ and $\displaystyle \omega_2$ respectively where $\displaystyle \omega_1 - \omega_2 = 1 kHz$. A detector receives the signals from the two stations simultaneously. It can only detect signals of intensity $\displaystyle &gt; 2A^2.$ Find the interval between successive maxima of the intensity of the signal received by the detector.

Question 43 : A string of length $l$ is fixed at both ends and is&#160;vibrating in second harmonic. The tension in string&#160;is $T$ and the linear mass density of string is $\mu$. The ratio of magnitude of maximum velocity of&#160;particle and the magnitude of maximum&#160;acceleration is<br/>

Question 44 : Amplitude of a travelling wave on a string is 1mm. If linear mass density of string is $10^{-4}kg $ $m^{-1} $ , tension in the string is $1N$ and frequency of vibration is $10Hz$, then average power needed to maintain such waves in string is : ($\pi^{2}=10$)<br/>

Question 45 : Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency ${\nu}_{1}$ and the other with frequency ${\nu}_{2}$. The ratio $ \dfrac{\nu _1}{\nu _2}$ is

Question 46 : The average power transmitted through a given point on a string supporting a sine wave is $0.40\ watt$ when the amplitude of wave is $2\ mm$. What average power will transmitted through this point its amplitudes is increased to $4\ mm$?

Question 47 : The frequency of the $1st$ harmonic of a sonometer&#160;wire is $160Hz$. If the length of the wire is increased&#160;by $50\%$ and the&#160;tension in the wire is decreased by $19\%$, the frequency of its first overtone is :&#160;( Assume linear mass density to be constant )

Question 48 : A light pointer fixed to one prong of a tuning fork touched a vertical plate. The fork is set vibrating and plate is allowed to fall freely. $8$ complete oscillations are counted when the plate falls through $10 cm$. What is the frequency of the tuning fork?

Question 49 : One end of a taut string of length $3 m$ along the x axis is fixed at $x$ $=$ $0$. The speed of the waves in the string is $100 ms^{-1}$. The other end of the string is vibrating in the y direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

Question 50 : Assertion: The decrease in speed of sound at high altitudes is due of fall in pressure at this altitude. Reason: The speed of sound is the same at all pressures and varies with temperature only.

Question 51 : The displacement $y$ of a particle, if given by $y=4\cos^2\left(\dfrac{t}{2}\right)\sin(1000t)$. This expression may be considered to be a result of the superposition of how many simple harmonic motions?

Question 52 : A wire of density $\rho $ is stretched between the clamps at a distance $L$ apart, while being subjected to an&#160;extension $l(l&lt;&lt;L),\ Y$ is the Young's modulus of the wire. The lowest resonant frequency of transverse&#160;vibration of the wire is approximately given by :<br/>

Question 53 : If for a particle moving in SHM, there is a sudden increase of $1$% in restoring force just as particle passing through mean position, percentage change in amplitude will be

Question 54 : The velocities of sound at the same temperature in two monoatomic gases of densities $p_1$ and $p_2$ are $v_1$ and $v_2$ respectively. If $p_1/p_2 = 4$, then the value of $v_1/v_2$ is

Question 55 : An object of specific gravity $p$ is hung from a thin steel wire. The fundamental frequency for transverse standing waves in the wire is $300\ Hz$. The object is immersed in water so that one half of its volume is submerged. The new fundamental frequency in $Hz$ is