The displacement $y$ (in $cm$) produced by a simple harmonic wave is $y = \frac{{10}}{\pi }\sin \left( {2000\pi t - \frac{{\pi x}}{{17}}} \right)$. The periodic time and maximum velocity of the particles in the medium will respectively be
Medium
Download our app for free and get started
(c) Comparing with $y = a\sin (\omega t - kx)$==>$a = \frac{{10}}{\pi },\omega = 2000\,\pi $
$\therefore $ ${v_{\max }} = a\omega = \frac{{10}}{\pi } \times 2000\,\pi = 200m/\sec $
and $\omega = \frac{{2\pi }}{T} \Rightarrow 2000\,\pi = \frac{{2\pi }}{T}$==> $T = {10^{ - 3}}\,sec$
Download our appand 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.*
Similar Questions
- 1The equations of two waves are given byView Solution
$y_{1}=5 \sin 2 \pi(x-v t) \,c m\,$
$y_{2}=3 \sin 2 \pi(x-v t+1.5) \,c m$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is.........$cm$
- 2A steel rod $100 \,cm$ long is clamped at its middle. The fundamental frequency of longitudinal vibrations of the rod are given to be $2.53\,kHz$. What is the speed of sound in steel ..... $km/sec$View Solution
- 3The displacement due to a wave moving in the positive $x-$direction is given by $y = \frac{1}{{(1 + {x^2})}}$ at time $t = 0$ and by $y = \frac{1}{{[1 + {{(x - 1)}^2}]}}$ at $t = 2$ seconds, where $x$ and $y$ are in metres. The velocity of the wave in $m/s$ isView Solution
- 4Vibrating tuning fork of frequency $n$ is placed near the open end of a long cylindrical tube. The tube has a side opening and is fitted with a movable reflecting piston. As the piston is moved through $8.75 cm$, the intensity of sound changes from a maximum to minimum. If the speed of sound is $350 \,m/s. $ Then $n$ is .... $Hz$View Solution
- 5A sinusoidal progressive wave is generated in a string. It’s equation is given by $y = (2\,\, mm) sin (2\pi x - 100 \pi t + \pi /3)$. The time when particle at $x = 4$ $m$ first passes through mean position, will beView Solution
- 6View Solutionstationary source is emitting sound at a fixed frequency $f_0$, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is $1.2\%$ of $f_0$. What is the difference in the speeds of the cars (in $km$ per hour) to the nearest integer ..... $km/hr$ ? The cars are moving at constant speeds much smaller than the speed of sound which is $330$ $ms^{-1}$.
- 7View SolutionWhen two sound waves are superimposed, beats are produced when they have
- 8The given diagram shows a detector placed between a transmitter of sound waves and a metal plate. At three adjacent points, $ R, S$ and $T$ , the meter shows zero intensity. Which of the following is the frequency of the emitted wave ... $Hz$ ? (Take the velocity of sound as $ = 300\ m/s$ )View Solution
- 9A source of sound $S$ is moving with a velocity $50m/s$ towards a stationary observer. The observer measures the frequency of the source as $1000 Hz$. What will be the apparent frequency of the source when it is moving away from the observer after crossing him .... $Hz$ $?$ The velocity of sound in the medium is $350 m/s$View Solution
- 10Two persons $A$ and $B$, each carrying a source of sound of frequency $n$, are standing a few metres apart in a quiet field. $A$ starts moving towards $B$ with a speed $u$. If $v$ is the speed of sound, the number of beats heard per second by $A$ will beView Solution