The equation of stationary wave along a stretched string is given by $y = 5\sin \frac{{\pi x}}{3}\cos 40\pi t$, where $x $ and $y$ are in $cm$ and $t$ in second. The separation between two adjacent nodes is..... $cm$
Medium
Download our app for free and get started
(b) On comparing the given equation with standard equation
.$y = 2a\sin \frac{{2\pi x}}{\lambda }\cos \frac{{2\pi vt}}{\lambda }$
==>$\frac{{2\pi x}}{\lambda } = \frac{{\pi x}}{3} \Rightarrow \lambda = 6$
Separation between two adjacent nodes = $\frac{\lambda }{2} = 3=\,cm$
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
- 1In a test of subsonic Jet flies over head at an altitude of $100\,\, m$. The sound intensity on the ground as the Jet passes overhead is $160 \,\,dB$. At what altitude should the plane fly so that the ground noise is not greater than $120\,\, dB.$View Solution
- 2A transverse wave propagating on the string can be described by the equation $y=2 \sin (10 x+300 t)$. where $x$ and $y$ are in metres and $t$ in second. If the vibrating string has linear density of $0.6 \times 10^{-3} \,g / cm$, then the tension in the string is .............. $N$View Solution
- 3Each 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
- 4The $(x, y)$ coordinates of the corners of a square plate are $(0, 0), (L, 0), (L, L)$ and $(0, L).$ The edges of the plate are clamped and transverse standing waves are set up in it. If $u(x, y)$ denotes the displacement of the plate at the point $(x, y)$ at some instant of time, the possible expression(s) for $u$ is(are) ($a =$ positive constant)View Solution
- 5$A$ is singing a note and at the same time $B$ is singing a note with exactly one-eighth the frequency of the note of $A$. The energies of two sounds are equal, the amplitude of the note of $B$ isView Solution
- 6A plane progressive wave is given by $y=2 \cos 2 \pi(330 t-x) m$. The frequency of the wave is:View Solution
- 7If the wave equation $y = 0.08\sin \frac{{2\pi }}{\lambda }(200t - x)$ then the velocity of the wave will beView Solution
- 8Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequecny of the new pipe so obtained will beView Solution
- 9The vibration of a string fixed at both ends are described by $Y= 2 \,\,sin(\pi x) \,\,sin\,\,(100\pi t)$ where $Y$ is in $mm$,$x$ is in $cm$,$t$ in $sec$ thenView Solution
- 10In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is $0.1\,m$. when this length is changed to $0.35\,m,$ the same tuning fork resonates with the first overtone. Calculate the end correction .... $m$View Solution