Download App
A transverse sinusoidal wave moves along a string in the positive $\mathrm{x}$-direction at a speed of $10 \mathrm{~cm} / \mathrm{s}$. The wavelength of the wave is $0.5 \mathrm{~m}$ and its amplitude is $10 \mathrm{~cm}$. At a particular time $t$, the snap -shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $5 \mathrm{~cm}$ is Figure: $Image$
  • A$\frac{\sqrt{3} \pi}{50} \hat{\mathrm{j}} \mathrm{m} / \mathrm{s}$
  • B$-\frac{\sqrt{3} \pi}{50} \hat{\mathrm{j}} \mathrm{m} / \mathrm{s}$
  • C$\frac{\sqrt{3} \pi}{50} \hat{\mathrm{i}} \mathrm{m} / \mathrm{s}$
  • D$-\frac{\sqrt{3} \pi}{50} \hat{i} \mathrm{~m} / \mathrm{s}$
IIT 2008, Advanced
art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Download App

Similar Questions

  • 1
    When two tuning forks (fork $1$ and fork $2$ ) are sounded together, $4$ beats per second are heard. Now some tape is attached on the prong of the fork $2$. When the tuning forks are sounded again, $6$ beats per second are heard. If the frequency of fork $1$ is $200 \,Hz$, then the original frequency of fork $2$ is ........... $Hz$
    View Solution
  • 2
    The figure represents the instantaneous picture of a transverse harmonic wave traveling along the negative $x$-axis. Choose the correct alternative $(s)$ related to the movement of the nine points shown in the figure.  The points moving downwards is/are
    View Solution
  • 3
    The fundamental frequency of a string stretched with a weight of $4 kg$ is $256 Hz$. The weight required to produce its octave is .... $kg \,wt$
    View Solution
  • 4
    A wave equation is

    $y = 10^{-4}\, sin\, (60\,t + 2x)$

    Where $x$ and $y$ are in $metres$ and $t$ is in $ec$ . Which of the following statements is correct ?

    View Solution
  • 5
    A string is fixed at both ends vibrates in a resonant mode with a separation $2.0 \,\,cm$ between the consecutive nodes. For the next higher resonant frequency, this separation is reduced to $1.6\,\, cm$. The length of the string is .... $cm$
    View Solution
  • 6
    The speed of sound in air at a given temperature is $350 m/s$. An engine blows whistle at a frequency of $1200 \,cps$. It is approaching the observer with velocity $50 m/s$. The apparent frequency in cps heard by the observer will be
    View Solution
  • 7
    What is the phase difference between two successive crests in the wave
    View Solution
  • 8
    Two sitar strings, $A$  and $B,$  playing the note $'Dha'$  are slightly out of tune and produce beats and frequency  $5\,Hz.$  The tension of the string $B$ is slightly increased and the beat frequency is found to decrease by  $3\,Hz$ . If the frequency of $A$ is $425\,Hz,$  the original frequency of $B$ is  ... $Hz$
    View Solution
  • 9
    If speed of sound in air in $330 \,m / s$ then, find the number of tones present in an open organ pipe of length $1\, m$ whose frequency if $\leq 1000$.
    View Solution
  • 10
    A tuning fork with frequency $800 \;\mathrm{Hz}$ produces resonance in a resonance column tube with upper end open and lower end closed by water surface. Surface. Successive resonance are observed at length $9.75 \;\mathrm{cm}, 31.25\; \mathrm{cm}$ and $52.75\; \mathrm{cm} .$ The speed of sound in air is ......$m/s$
    View Solution