Two waves $y_1=\mathrm{A} \cos (0.5 \pi x-100 \pi t)$ and $y_2=\mathrm{A} \cos (0.467 \pi x-92 \pi t)$ are travelling in a pipe placed along $x$-axis.

Find the number of times $y_1+y_2=0$ at $x=0$ in $1 s$.

A whistling train approaches a junction. An observer standing at the junction observes the frequency to be 2.2 kHz and 1.8 kHz of the approaching and the receding train. Find the speed of the train (speed of sound = 300 m/s).

A transverse harmonic disturbance is produced in a string. The maximum transverse velocity is 3 m/s and the maximum transverse acceleration is 90 m/s$$^2$$ . If the wave velocity is 20 m/s, then find the waveform.