A travelling wave represented by $y = A \sin (\omega t - kx )$ is susperimposed on another wave represented by $y = A$ $\sin (\omega t + kx )$. The resultant is
AIEEE 2011, Medium
Download our app for free and get started
$Y=A \sin (\omega t-k x)+A \sin (\omega t+k x)$
$Y=2 A \sin \omega t$ coskx standing wave
For nodes coskx $=0$
$\frac{2 \pi}{\lambda} \cdot x=(2 n+1) \frac{\pi}{2}$
$x=\frac{(2 n+1) \lambda}{4}, n=0,1,2,3, \ldots \ldots$
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
- 1An observer standing near the sea shore observes $54$ waves per minute. If the wavelength of the water wave is $10m$ then the velocity of water wave is .... $ms^{-1}$View Solution
- 2The ratio of maximum to minimum intensity due to superposition of two waves is $\frac{{49}}{9}$ Then the ratio of the intensity of component waves is .View Solution
- 3An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be $\dots \;$%View Solution
- 4Ten tuning forks are arranged in increasing order of frequency in such a way that any two nearest tuning forks produce $4$ beats/sec. The highest frequency is twice of the lowest. Possible highest and the lowest frequencies areView Solution
- 5A point source emits sound equally in all directions in a non-absorbing medium, Two points $P$ and $Q $ are at distance of $2m$ and $3m$ respectively from the source. The ratio of the intensities of the waves at $P$ and $ Q$ isView Solution
- 6A uniform tube of length $60.5\,cm$ is held vertically with its lower end dipped in water. A sound source of frequency $500\,Hz$ sends sound waves into the tube. When the length of tube above water is $16\,cm$ and again when it is $50\,cm,$ the tube resonates with the source of sound. Two lowest frequencies (in $Hz$), to which tube will resonate when it is taken out of water, are (approximately).View Solution
- 7A certain string will resonant to several frequencies, the lowest of which is $200 \,cps$. What are the next three higher frequencies to which it resonants?View Solution
- 8A wave has velocity $u$ in medium $P$ and velocity $2u$ in medium $Q.$ If the wave is incident in medium $P$ at an angle of $30°$ then the angle of refraction will be .... $^o$View Solution
- 9The path Difference between the two waves ${y_1} = {a_1}\,\sin \,\left( {\omega t - \frac{{2\pi x}}{\lambda }} \right)$ and ${y_2} = {a_2}\,\cos \,\left( {\omega t - \frac{{2\pi x}}{\lambda } + \phi } \right)$ isView Solution
- 10A transverse wave of frequency $500 \,Hz$ and speed $100 \,m / s$ is travelling in the positive $x$-direction on a long string. At time $t=0 \,s$, the displacements at $x=0.0 \,m$ and at $x=0.25 \,m$ are $0.0 \,m$ and $0.02 \,m$, respectively. The displacement at $x=0.2 \,m$ at $t=5 \times 10^{-4} s$ is ............ $m$View Solution