The stationary wave produced on a string is represented by the equation $y = 5\cos (\pi x/3)\sin 40\pi \,t$. Where $x$ and $y$ are in cm and $t$ is in seconds. The distance between consecutive nodes is .... $cm$
A$5 $
B$\pi $
C$3$
D$40 $
Easy
Download our app for free and get started
C$3$
c (c) On comparing the given equation with standard equation
Hence, distance between two consecutive nodes $\lambda = 3\, cm$
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.*
A string fixed at one end is vibrating in its second overtone. The length of the string is $10\ cm$ and maximum amplitude of vibration of particles of the string is $2\ mm$ . Then the amplitude of the particle at $9\ cm$ from the open end is
A train blowing its whistle moves with constant speed on a straight track towards observer and then crosses him. If the ratio of difference between the actual and apparent frequencies be $3: 2$ in the two cases, then the speed of train is [ $v$ is speed of sound]
A tuning fork of frequency $392 Hz,$ resonates with $50 cm $ length of a string under tension ($T$). If length of the string is decreased by $2\%$, keeping the tension constant, the number of beats heard when the string and the tuning fork made to vibrate simultaneously is
A wave travelling in the $+ve$ $x-$ direction having displacement along $y-$ direction as $1\,\, m,$ wavelength $2\pi\,\, m$ and frequency of $\frac{1}{\pi}$ $Hz$ is represented by
$25$ tunning forks are arranged in series in the order of decreasing frequency. Any two successive forks produce $3\, beats/sec.$ If the frequency of the first turning fork is the octave of the last fork, then the frequency of the $21^{st}$ fork is .... $Hz$
Two open organ pipes give $4$ beats/sec when sounded together in their fundamental nodes. If the length of the pipe are $100 cm$ and $102.5 cm$ respectively, then the velocity of sound is ..... $m/s$
On a long horizontally moving belt, a child runs to and fro with a speed $9\, km\, h^{-1}$ (with respect to the belt) between his father and mother located $50\, m$ apart on the moving belt. The belt moves with a speed of $4\, km\, h^{-1}$. For an observer on a stationary platform, the speed of the child running in the direction of motion of the belt is ..... $km\,h^{-1}$