MCQ
The equation of a longitudinal wave is represented as $y = 20\cos \pi (50t - x)$. Its wavelength is ..... $cm$
  • A
    $5$
  • $2$
  • C
    $50$
  • D
    $20$

Answer

Correct option: B.
$2$
b
(b) By comparing it with standard equation

$y = a\cos (\omega t - kx)$

==>$k= \frac{{2\pi }}{\lambda } = \pi $

==> $\lambda = 2\,cm$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The components of a force acting on a particle are varying according to the graphs shown. To reach at point $B\, (8, 20, 0)$ from point $A\,(0, 5, 12)$ the particle moves on paths parallel to $x-$ axis then $y-$ axis and then $z-$ axis, then work done by this force is ............ $\mathrm{J}$
A cyclist on a level road takes a sharp circular turn of radius $3 \;m \;\left( g =10 \;ms ^{-2}\right)$. If the coefficient of static friction between the cycle tyres and the road is $0.2$, at which of the following speeds will the cyclist not skid while taking the turn?
A particle of mass m is attached to a spring (of spring constant k) and has a natural angular frequency ${\omega _0}$ - An external force $F (t)$ proportional to $\cos \omega \,t((\omega \ne {\omega _0})$ is applied to the oscillator. The time displacement of the oscillator will be proportional to
The unit of "impulse per unit area" is same as that of
A particle is projected horizontally from a tower with velocity $10\,m / s$. Taking $g=10\,m / s ^2$. Match the following two columns at time $t=1\,s$.
Column $I$ Column $II$
$(A)$ Horizontal component of velocity $(p)$ $5$ SI unit
$(B)$ Vertical component of velocity $(q)$ $10$ SI unit
$(C)$ Horizontal displacement $(r)$ $15$ SI unit
$(D)$ Vertical displacement $(s)$ $20$ SI unit
Two spherical vessel of equal volume, are connected by a n arrow tube. The apparatus contains an ideal gas at one atmosphere and $300K$. Now if one vessel is immersed in a bath of constant temperature $600K$ and the other in a bath of constant temperature $300K$. Then the common pressure will be ...... $atm$
A particle of mass $m$ moves around the origin in a potential $\frac{1}{2} m \omega^{2} r^{2}$, where $r$ is the distance from the origin. Applying the Bohr's model in this case, the radius of the particle in its $n$th orbit in terms of $a=\sqrt{h /(2 \pi m \omega)}$ is
A tuning fork gives $4$ beats with $50\, cm$ length of a sonometer wire if the length of  the wire is shortened by $1\, cm$. the no. of beats still the same. The frequency of the  fork is -............. $\mathrm{Hz}$
particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec a\, = \,(4\hat i + 3\hat j)\,\,m/{s^2}$ and $\vec P\, = \,(8\hat i\, - \,6\hat j)\,kg\, - \,m/s$ . The motion of the particle is
Two simple harmonic motions of angular frequency $100$ and $1000\,\,rad\,s^{-1}$ have the same displacement amplitude. The ratio of their maximum acceleration is