The equation of a wave disturbance is given as : $y = 0.02 cos \left( {\frac{\pi }{2} + 50\pi t} \right) cos (10 x),$ where $x$ and $y$ are in meters and $t$ in seconds. Choose the wrong statement:
Medium
Download our app for free and get started
$y=0.02 \cos (\pi / 2+50 \pi \times t) \cos (10 \pi \times x)$
At $x=0.3\,m$
$y=0.02 \cos (\pi / 2+50 \pi \times t) \cos (3 \pi)=-0.02 \cos (\pi / 2+50 \pi \times t)$ (It is
right)
Now compare the given equation by the standard stationary wave equation,
$y=A \cos (\phi+\omega \times t) \cos (2 \pi \lambda \times x)$
$2 \pi \lambda=10 \pi, \lambda=0.2\,m$ (it is also right)
$\text { At } x=0.15\,m$
$y=0.02 \cos (\pi / 2+50 \pi \times t) \cos (\pi / 2)$
and
$v = A \omega=0.02 * 50 \pi=\pi ms ^{-1}$
Hence, option " $C$ " is wrong.
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 amplitude of wave disturbance propagating in the positive $x$-direction is given by $y=\frac{1}{(1+x)^{2}}$ at time $t=0$ and $y=\frac{1}{1+(x-2)^{2}}$ at $t=1$ s, where $x$ and $y$ are in metres. The shape of wave does not change during the propagation. The velocity of the wave will be $...\,{m} / {s}.$View Solution
- 2The number of beats produced per second by two vibrations: $x_1 =x_0$ sin $646\pi t$ and $x_2 = x_0 sin 652 \pi t$ isView Solution
- 3A wave travelling along the $x-$axis is described by the equation $y\left( {x,t} \right) = 0.005cos\left( {\alpha x - \beta t} \right)$ If the wavelength and the time period of the wave are $0.08\ m$ and $2.0\ s$, respectively, then $\alpha$ and $\beta$ in appropriate units areView Solution
- 4The two nearest harmonics of a tube closed at one end and open at other end are $220\,\, Hz$ and $260\,\, Hz.$ What is the fundamental frequency of the system .... $Hz$ ?View Solution
- 5This 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 $1:$ In the resonance tube experiment, if the tuning fork is replaced by another identical turning fork but with its arm having been filled, the length of the air column should be increased to obtain resonance again.
Statement $2:$ On filling the arms, the frequency of a tuning fork increases.
- 6A closed pipe of length $10 \,cm$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe ......... $cm$View Solution
- 7Two sources of sound placed close to each other, are emitting progressive waves given by $ y_1=4sin\left( {600\pi t} \right)$ and $y_2=5sin\left( {608\pi t} \right)$ An observer located near these two sources of sound will hearView Solution
- 8If ${n_1},{n_2},{n_3}.........$ are the frequencies of segments of a stretched string, the frequency $n$ of the string is given byView Solution
- 9In the resonance tube experiment, first resonant length is $l_1$ and second resonant length is $l_2$ then the third resonant length will beView Solution
- 10A closed organ pipe has a fundamental frequency of $1.5\, kHz$. The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person can hear is $20,000\, Hz$)View Solution