A progressive wave travelling in positive $x$-direction given by $y=a \cos (k x-\omega t)$ meets a denser surface at $x=0, t=0$. The reflected wave is then given by
KVPY 2009, Medium
Download our app for free and get started
(c)
Due to hard boundary reflection, phase of wave changes by $\pi$ radians and its direction of travel is reversed.
So, resultant wave is
$y=a \cos (k x+\omega t+\pi)$
$\Rightarrow y=-a \cos (k x+\omega t)$
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 equation of a longitudinal wave is represented as $y = 20\cos \pi (50t - x)$. Its wavelength is ..... $cm$View Solution
- 2View SolutionIf you set up the ninth harmonic on a string fixed at both ends, its frequency compared to the seventh harmonic
- 3At standard temperature and pressure the density of a gas is $1.3$ $kg/{m^3}$ and the speed of the sound in gas is $330\, m/sec.$ Then the degree of freedom of the gas will beView Solution
- 4The ends of stretched wire of length $L$ are fixed at $x\, = 0$ and $x \,= L$. In one experiment, the displacement of the wire is ${y_1} = A\sin\, \left( {\pi x/L} \right)\sin \,\omega t$ and energy is $E_1$. and in another experiment its displacement is ${y_2} = A\sin \,\left( {2\pi x/L} \right)\sin 2\omega t$ and energy is $E_2$, ThenView Solution
- 5$5\, beats/ second$ are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either $0.95\,m$ or $1\,m$ . The frequency of the fork will be ... $Hz$View Solution
- 6A tuning fork makes $256$ vibrations per second in air. When the velocity of sound is $330\, m/s$, then wavelength of the tone emitted is ... $m$View Solution
- 7A standing wave pattern of amplitude $A$ in a string of length $L$ shows $2$ nodes (plus those at two ends). If one end of the string corresponds to the origin and $v$ is the speed of progressive wave, the disturbance in the string, could be represented (with appropriate phase) as:View Solution
- 8In a resonance tube experiment when the tube is filled with water up to height of $17.0\, cm$ from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of $24.5\, cm$. If the velocity of sound in air is $330\, m / s ,$ the tuning fork frequency is$......Hz$View Solution
- 9Each of the two strings of length $51.6\,\, cm$ and $49.1\,\, cm$ are tensioned separately by $20\,\, N$ force. Mass per unit length of both the strings is same and equal to $1\,\, g/m.$ When both the strings vibrate simultaneously the number of beats isView Solution
- 10A resonance air column of length $20 cm$ resonates with a tuning fork of frequency $250 Hz$. The speed of sound in air is .... $m/s$View Solution