A wave motion has the function $y = {a_0}\sin (\omega \,t - kx)$. The graph in figure shows how the displacement $y$ at a fixed point varies with time $t$. Which one of the labelled points shows a displacement equal to that at the position $x = \frac{\pi }{{2k}}$ at time $t = 0$
Medium
Download our app for free and get started
(b) At $t = 0$ and $x = \frac{\pi }{{2k}}$. The displacement
$y = {a_0}\sin \,\left( {\omega {x_0} - k \times \frac{\pi }{{2x}}} \right) = - {a_0}\sin \frac{\pi }{2} = - {a_0}$
from graph. Point of maximum displacement $(a_0)$ in negative direction is $Q.$
$y = {a_0}\sin \,\left( {\omega {x_0} - k \times \frac{\pi }{{2x}}} \right) = - {a_0}\sin \frac{\pi }{2} = - {a_0}$
from graph. Point of maximum displacement $(a_0)$ in negative direction is $Q.$
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
- 1A plane wave is described by the equation $y = 3\cos \left( {\frac{x}{4} - 10t - \frac{\pi }{2}} \right)$. The maximum velocity of the particles of the medium due to this wave isView Solution
- 2A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle $60^o$ with ground level. But he finds the aeroplane right vertically above his position. If $\upsilon $ is the speed of sound, speed of the plane isView Solution
- 3The wavelength is $120 cm$ when the source is stationary. If the source is moving with relative velocity of $60\, m/sec$ towards the observer, then the wavelength of the sound wave reaching to the observer will be ... $cm$ (velocity of sound $= 330 \,m/s$)View Solution
- 4A boat at anchor is rocked by waves whose crests are $100\, m$ apart and velocity is $25\, m/sec$. The boat bounces up once in every: ... $sec$View Solution
- 5The sound intensity level at a point $4 \,m$ from the point source is $10 \,dB$, then the sound level at a distance $2 \,m$ from the same source will be ........ $dB$View Solution
- 6This question has Statement $1$ and Statement $2$ .Of the four choices given after the Statements, choose the one that best describes the two Statements.View Solution
Statement $1$ : Bats emitting ultrasonic waves can detect the location of a prey by hearing the waves reflected from it.
Statement $2$ : When the source and the detector are moving, the frequency of reflected waves is changed - 7An observer moves towards a stationary source of sound with a speed $1/5^{th}$ of the speed of sound. The wavelength and frequency of the source emitted are $\lambda $ and $f$ respectively. The apparent frequency and wavelength recorded by the observer are respectivelyView Solution
- 8When a tuning fork $A$ of unknown frequency is sounded with another tuning fork $B$ of frequency $256 Hz$, then $3$ beats per second are observed. After that $A$ is loaded with wax and sounded, the again $3$ beats per second are observed. The frequency of the tuning fork $A$ is ..... $Hz$View Solution
- 9View SolutionThe beats are produced by two sound sources of same amplitude and of nearly equal frequencies. The maximum intensity of beats will be ...... that of one source
- 10Frequency of tuning fork $A$ is $256\,Hz$ . It produces four $beats/sec$ . with tuning fork $B$ . When wax is applied at tuning fork $B$ then $6\,beats/sec$ . are heard. By reducing little amount of wax $4\,beats/sec$ . are heard. Frequency of $B$ is .... $Hz$View Solution