A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$, is produced at the lower end of the rope. The wave length of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2\,/\,\lambda _1$ is
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A vibrating tuning fork is moving slowly and uniformly in a horizontal circular path of radius $8\,m$. The shortest distance of an observer in same plane from the tuning fork is $9 \,m$. The distance between the tuning fork and observer at the instant when apparent frequency becomes maximum is ......... $m$
A plane progressive wave is represented by the equation $y = 0.1\sin \left( {200\pi t - \frac{{20\pi x}}{{17}}} \right)$ where y is displacement in $m$, $ t$ in second and $x$ is distance from a fixed origin in meter. The frequency, wavelength and speed of the wave respectively are
A speeding motorcyclist sees traffic jam ahead him. He slows down to $36\,\, km\,\,hour^{-1}$ He finds that traffic has eased and a car moving ahead of him at $18 \,\, km\,\,hour^{-1}$ is honking at a frequency of $1392\,\, Hz.$ If the speed of sound is $343\, m s^{-1}$, the frequency of the honk as heard by him will be .... $Hz$
A wave is given by $y = 3\sin 2\pi \left( {\frac{t}{{0.04}} - \frac{x}{{0.01}}} \right)$, where $y$ is in $cm$. Frequency of wave and maximum acceleration of particle will be
The equation of displacement of two waves are given as ${y_1} = 10\sin \left( {3\pi t + \frac{\pi }{3}} \right)$; ${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$. Then what is the ratio of their amplitudes
One 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.
In a resonance tube the first resonance with a tuning fork occurs at $16 cm$ and second at $49 cm.$ If the velocity of sound is $330 m/s,$ the frequency of tuning fork is