Two sound waves travelling in the same direction have displacements $y_1 = a \sin(0.2 \pi x - 50 \pi t)$ and $y_2 = a \sin(0.15 \pi x - 46 \pi t)$. How many times can a listener hear sound of maximum intensity in one second?

Two sound waves with wavelengths $5.0\, m$ and $5.5\, m$ respectively,each propagate in a gas with velocity $330\, m/s$. We expect the following number of beats per second.

$A$ tuning fork of frequency $392 \, Hz$ resonates with $50 \, cm$ length of a string under tension $T$. If the length of the string is decreased by $2 \%$,keeping the tension constant,the number of beats heard when the string and the tuning fork are made to vibrate simultaneously is

$56$ tuning forks are arranged such that each fork produces $4$ beats per second with its previous one. If the frequency of the last fork is twice that of the first, the frequency of the $19^{\text{th}}$ fork is . . . . . . (in $\text{Hz}$)

Draw graphs of beats produced by two harmonic waves of frequency $11 \ Hz$ and $9 \ Hz$.

$A$ source of unknown frequency gives $4\, \text{beats/s}$ when sounded with a source of known frequency $250\, \text{Hz}.$ The second harmonic of the source of unknown frequency gives $5\, \text{beats/s}$ when sounded with a source of frequency $513\, \text{Hz}.$ The unknown frequency is .... $\text{Hz}$