Two tuning forks of frequencies $320 \,Hz$ and $480 \,Hz$ are sounded together to produce sound waves. The velocity of sound in air is $320 \,ms^{-1}$. The difference between the wavelengths of these waves is nearly: (in $cm$)

Two sound waves having wavelengths $5.0 \ m$ and $5.5 \ m$ propagate in a gas with velocity $300 \ m/s$. The number of beats produced per second is

$A$ sound wave travels with a velocity of $300 \, m \, s^{-1}$ through a gas. $9$ beats are produced in $3 \, s$ when two waves pass through it simultaneously. If one of the waves has a wavelength of $2 \, m$, the wavelength of the other wave is ..... $m$.

The displacement equations of sound waves produced by two sources are given by $y_1 = 5 \sin(400 \pi t)$ and $y_2 = 8 \sin(408 \pi t)$, where $t$ is time in seconds. If the waves are produced simultaneously, the number of beats produced per minute is

$A$ tuning fork whose frequency as given by the manufacturer is $512 \ Hz$ is being tested with an accurate oscillator. It is found that the fork produces a beat of $2 \ Hz$ when the oscillator reads $514 \ Hz$,but produces a beat of $6 \ Hz$ when the oscillator reads $510 \ Hz$. The actual frequency of the fork is ..... $Hz$.

The frequency of a tuning fork is $220 \,Hz$ and the velocity of sound in air is $330 \,m/s$. When the tuning fork completes $80$ vibrations, the distance travelled by the sound wave is: (in $\,m$)