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Questions Related to physics

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

An open tube is in resonance with string (frequency of vibration of tube in $n _{0}$. If tube is dipped on water is that 75% of length of tube is inside water, then the ratio of the frequency of tube to string now will be 

  1. 1

  2. 2

  3. $\dfrac{2}{3}$

  4. $\dfrac{3}{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
For open tube no $ = \dfrac{V}{2l} $
For closed tube length available for resonance
$ l^{1} ,l\times \dfrac{25}{100} = \frac{l}{4} $
fundamental frequency of water filled tube 
$ n _{1}\dfrac{V}{4l^{1}} = \frac{V}{4(l/4)} $ $(\because l^{1}= l/4) $
$ \therefore \dfrac{V}{l} = 2n _{0} = 1 $
$ = \dfrac{n}{n _{0}} = 2 $
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The equation of a standing wave in a string fixed at both ends is given as $ y =  A \quad sin \quad  kx \quad cos \quad \omega t $
The amplitude and frequency of a particle vibrating at the mid of an antiode and a node are respectively

  1. $A,\dfrac{\omega }{{2\pi }}$

  2. $\dfrac{A}{{\sqrt 2 }},\dfrac{\omega }{{2\pi }}$

  3. $A,\dfrac{\omega }{{\pi }}$

  4. $\sqrt 2 A,\dfrac{\omega }{{2\pi }}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A wire of length l , area of cross section A  and young's modules of elasticity  y is  suspended from the roof of a building. A  block of mass m is attached at lower end of the wire. if the block is displaced from its mean position and then released the block starts  oscillating. Time period of these oscillation will be

  1. $2\pi \sqrt { \frac { Al }{ mY } } $

  2. $2\pi \sqrt { \frac { AY }{ ml } } $

  3. $2\pi \sqrt { \frac { ml }{ YA } } $

  4. $2\pi \sqrt { \frac { m }{ YAl } } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

Which of the following equations represents a transverse wave travelling along -y axis?

  1. $x = A\sin\ (\omega t\ -\ ky)$

  2. $x= A\ sin\ (\omega t\ +\ ky)$

  3. ${ y } _{ 0 }\ =A\sin\ (\omega t - kX   )$

  4. ${ y } _{ 0 } = A\ sin (\omega t + kX )$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\begin{array}{l} For\, \, negative\, \, y-axis \ sign\, \, of\, \, \omega t\, \, & \, \, ky\, \, should\, \, be\, \, same\,  \ x=A\sin  \left( { \omega t+ky } \right)  \ Hence, \ option\, \, B\, \, is\, correct\, \, naswer. \end{array}$

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The displacement from the position of equilibrium of a point $4\ cm$ from a source of sinusoidal oscillations is half the amplitude at the moment $t=\dfrac{T}{6} (T$ is the time period$)$. Assume that the source was at mean position at $t=0$. The wavelength of the running wave is 

  1. $0.96\ m$

  2. $0.48\ m$

  3. $0.24\ m$

  4. $0.12\ m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Going by the data given to us, this wave is sinusoidal in nature and the wave equation takes the form of
$y = A\sin( \omega t - kx),$ as it is given that at $t = 0,$  the source is at mean position.
Here$,\ x = 4\ cm = 0.04\ m$
$y = A/2$
Amplitude $= A$
$t = \dfrac{T}{6}$
We know that $ \omega  = 2 \dfrac{ \pi }{T}$
$\Rightarrow \dfrac{A}{2} = A\sin((2  \pi  / T)(T/6) - 0.04k)$
$\sin((2 \pi  / T)(T/6) - 0.04k) = 1/2$
$\Rightarrow ((2  \pi / T)(T/6) - 0.04k) =  \pi / 6$
$k =  \pi  / 0.24$
wavelength $ \lambda = 2\pi  / k = 0.48\ m$

Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

A string of length 1 m fixed at one end and on the other end a block of mass M=4 kg is suspended.The string is set into vibrations and represented by equation, Y=$6\sin \left( {\dfrac{{\pi x}}{{10}}} \right)\;\cos \;100\;\pi t,$  where x and y are in cm an in seconds.
Find the number of loops formed in the string.

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The $(x, y)$ co-ordinates of the corners of a square plate are $(0, 0) (L, 0) (L, L)$ & $(0, L)$. The edges of the plate are clamped & transverse standing waves are set up in it. If $u (x, y)$ denotes the displacement of the plate at the point $(x, y)$ at some instant of time, the possible expression(s) for $u$ is/are : ($a$ = positive constant) 

  1. $a\displaystyle \cos \left(\dfrac{\pi x}{2 L}\right)$ $\displaystyle \cos \left(\dfrac{\pi y}{2 L}\right)$

  2.  $a\displaystyle \sin \left(\dfrac{\pi x}{L}\right)$ $\displaystyle \sin \left(\dfrac{\pi y}{L}\right)$

  3. $a\displaystyle \sin \left(\dfrac{\pi x}{L}\right)$ $\displaystyle \sin \left(\dfrac{2\pi y}{L}\right)$

  4.  $a\displaystyle \cos \left(\dfrac{2\pi x}{L}\right)$ $\displaystyle \sin \left(\dfrac{\pi y}{L}\right)$
Reveal answer Fill a bubble to check yourself
B,C Correct answer
Explanation
The expression for $u(x,y)$ should satisfy the following conditions-
i) $u=0$ at $x=0$ and at $y=0$
ii) $u=0$ at $x=L$ and at $y=L$
Only choices B and C satisfy this condition.
Multiple choice physics wave motion wave velocity speed and acceleration of travelling wave speed of a travelling wave

The displacement of the particle at $x=0$ of a stretched string carrying wave in the positive x-direction is given $f(t)=A sin \frac {t} {T})$. The wave speed is V. Write the wave equation 

  1. $f(x,t)=A sin (\frac {t} {T}) - (\frac{x} {V})$

  2. $f(x,t)=A sin (\frac {t} {T}) + (\frac{x} {VT})$

  3. $f(x,t)=A sin (t+- (\frac{x} {V})$

  4. $f(x,t)=A sin (\frac {t} {T}) - (\frac{x} {VT})$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a wave traveling in the positive x-direction, the function is f(t - x/v). Given f(t) = A sin(t/T), the wave equation is f(x, t) = A sin((t - x/v) / T) = A sin(t/T - x/(vT)).