A string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of transverse wave along the string at a distance $'x'$ from the free end will be
$\sqrt {gx} $
$\sqrt {2gx} $
$2\sqrt {gx} $
$\sqrt {2g(L - x)} $
A car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. Speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is ...... $Hz$
The apparent frequency of a sound wave as heard by an observer is $10\%$ more than the actual frequency. If the velocity of sound in air is $330\, m/sec$, then
$(i)$ The source may be moving towards the observer with a velocity of $30\,ms^{-1}$
$(ii)$ The source may be moving towards the observer with a velocity of $33\,ms^{-1}$
$(iii)$ The observer may be moving towards the source with a velocity of $30\,ms^{-1}$
$(iv)$ The observer may be moving towards the source with a velocity of $33\,ms^{-1}$
$56$ tuning forks are so arranged in increasing order of frequencies in series that each fork gives $4$ beats per second with the previous one. The frequency of the last fork is the octave of the first. The frequency of the first fork is ..... $Hz$
Two tuning forks $A$ and $B$ produce $8\, beats/s$ when sounded together. $A$ gas column $37.5\, cm$ long in a pipe closed at one end resonate to its fundamental mode with fork $A$ whereas a column of length $38.5 \, cm$ of the same gas in a similar pipe is required for resonance with fork $B$. The frequencies of these two tuning forks, are
The amplitude of a wave represented by displacement equation $y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be