Show that the slope of a transverse wave at any point on it is numerically equal to the ratio of particle speed at that point to the wave speed through the medium.

Explain what will happen to the pitch of the fundamental note emitted by an open organ pipe when

(i) air in it is replaced by carbon dioxide.

Explain what will happen to the pitch of the fundamental note emitted by an open organ pipe when

(ii) hot air is blown in the pipe.

Explain what will happen to the pitch of the fundamental note emitted by an open organ pipe when

(iii) greater amount of moisture is introduced in the tube.

State whether true or false:

(a) The ratio of the velocity of sound in hydrogen gas $\left(\gamma =\frac{7}{5}\right)$ to that in helium gas $\left(\gamma =\frac{5}{3}\right)$ at the same temperature is $\sqrt{\frac{12}{5}}$.