A wave travelling in the $-ve\,\,z-$ direction having displacement along $x-$ direction as $1\,m,$ wavelength $\pi\, m$ and frequency at $\frac {1}{\pi }\,H_Z$ is represented by
$x = sin\,(2t + 2z)$
$z = sin\,(2t + 2x)$
$x = sin\,(2\pi t -2z)$
$z = sin\,(2t -2x)$
Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t.$ Number of beats produced per minute is
Fundamental frequency of a sonometer wire is $n$. If the length and diameter of the wire are doubled keeping the tension same, then the new fundamental frequency is
When two sound sources of the same amplitude but of slightly different frequencies $v_1$ and $v_2$ are sounded simultaneously, the sound one hears has a frequency equal to
A small source of sound moves on a circle as shown in the figure and an observer is standing on $O.$ Let $n_1,\, n_2$ and $n_3$ be the frequencies heard when the source is at $A, B$ and $C$ respectively. Then
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 wavelength of the pulse when it reaches the top of the rope is $\lambda _2$ . The ratio $\lambda _2/\lambda _1$ is