A racing car moving towards a cliff sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If $v$ is the velocity of sound, the velocity of the car will be

Four tuning forks of frequencies $200,201, 204$ and $206\, Hz$ are sounded together.  The beat frequency will be

The phase difference between two points separated by $0.8 m$ in a wave of frequency $120 Hz$ is ${90^o}$. Then the velocity of wave will be ............ $\mathrm{m/s}$

Two vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $f_1$ and the other with frequency $f_2$. The ratio $\frac{f_1}{f_2}$ is given by

$56$ 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 ..... $Hz$

The two waves represented by $y_1 = a\,sin(\omega\,t)$ and $y_2 = b\, cos\, (\omega\, t)$ have a phase difference of