A standing wave is represented by
$Y = A\sin (100t)\cos (0.01x)$
where $Y$ and $A$ are in millimetre, $t$ is in seconds and $x$ is in metre. The velocity of wave is ..... $m/s$
AIPMT 1994, Easy
Download our app for free and get started
(a) By comparing given equation with $y = a\sin (\omega t)\cos kx$
==>$v = \frac{\omega }{k} = \frac{{100}}{{0.01}} = {10^4}$$m/s$
==>$v = \frac{\omega }{k} = \frac{{100}}{{0.01}} = {10^4}$$m/s$
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 acting in perpendicular directions are given as $x=a \cos (\omega t+\delta)$ and $y=a \cos (\omega t+\alpha)$, where $\delta=\alpha+\frac{\pi}{2}$, the resultant wave representsView Solution
- 2A rod of length $1.2\,m$ is clamped at the mid point and its fundamental frequency is $2\,MHz$ , then speed of wave inside the rod?View Solution
- 3The number of possible natural oscillations of air column in a pipe closed at one end of length $85 \,\,cm$ whose frequencies lie below $1250\,\, Hz$ are (Velocity of sound $= 340 \,\,m s^{-1}$)View Solution
- 4View SolutionIn a standing wave on a string.
- 5The equation of a travelling wave is given by$y = 0.5\sin (20x - 400t)$ where $x$ and $y$ are in meter and $t$ is in second. The velocity of the wave is .... $m/s$View Solution
- 6One insulated conductor from a household extension cord has a mass per unit length of $μ.$ A section of this conductor is held under tension between two clamps. A subsection is located in a magnetic field of magnitude $B$ directed perpendicular to the length of the cord. When the cord carries an $AC$ current of $"i"$ at a frequency of $f,$ it vibrates in resonance in its simplest standing-wave vibration state. Determine the relationship that must be satisfied between the separation $d$ of the clamps and the tension $T$ in the cord.View Solution
- 7View SolutionA transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant, among the following, choose the wrong statement.
- 8Two loudspeakers $M$ and $N$ are located $20 \mathrm{~m}$ apart and emit sound at frequencies $118 \mathrm{~Hz}$ and $121 \mathrm{~Hz}$, respectively. $A$ car is initially at a point $P, 1800 \mathrm{~m}$ away from the midpoint $Q$ of the line $M N$ and moves towards $Q$ constantly at $60 \mathrm{~km} / \mathrm{hr}$ along the perpendicular bisector of $M N$. It crosses $Q$ and eventually reaches a point $R, 1800(m$ away from $Q$. Let $v(t)$ represent the beat frequency measured by a person sitting in tlie car at time $t$. Let $v_P, v_Q$ and $v_R$ be the beat frequencies measured at locations $P . Q$ and $R$, respectively. The speed of sound in air is $330 \mathrm{~m} \mathrm{~s}^{-1}$. Which of the following statement($s$) is(are) true regarding the sound heard by the person?View Solution
($A$) $v_P+v_R=2 v_Q$
($B$) The rate of change in beat frequency is maximum when the car passes through $Q$
($C$) The plot below represents schematically the variation of beat frequency with time
(image)
($D$) The plot below represents schematically the variation of beat frequency with time
(image)
- 9View SolutionNewton assumed that sound propagation in a gas takes under
- 10A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T$ ($Y$ = young’s modulus, $\rho$ = density, $\alpha$ = coefficient of linear expansion) then the frequency of transverse vibration is proportional to :View Solution