Waves PYQs - Last 5 Years

For sound waves, if the number of nodes for the $5^{\text {th }}$ harmonic of an open-ended pipe is $n$ and that for the $9^{\text {th }}$ harmonic of the same pipe with one of its ends closed is $m$, the ratio $\frac{n}{m}$ is

For a travelling harmonic wave
$y(x, t)=2.0 \cos 2 \pi(10 t-0.0080 x+0.35)$, where $x$ and $y$ are in cm and $t$ in $s$. The phase difference between oscillatory motion of two points separated by a distance of 0.5 m is:

 A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:

The displacement of a travelling wave \(y=C \sin \frac{2 \pi}{\lambda}\) (at \(-x\)) where \(t\) is time, \(x\) is distance and \(\lambda\) is the wavelength, all in S.I. units. Then the frequency of the wave is

The \(4^{\text {th }}\) overtone of a closed organ pipe is same as that of \(3^{\text {rd }}\) overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is :

The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is

An organ pipe filled with a gas at 27\(^\circ\)C resonates at 400 Hz in its fundamental mode. If it is filled with the same gas at 90\(^\circ\)C, the resonance frequency at the same mode will be

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is