### Sound Waves

goals
Two trains $A$ and $B$ are moving with speeds $20\ m/s$ and $30\ m/s$ respectively in the same direction on the same straight track, with $B$ ahead of $A$. The engines are at the front ends. The engine of train $A$ blows a long whistle.
Assume that the sound of the whistle is composed of components varying in frequency from $f_{1}=800\ Hz$ to $f_{2}=1120\ Hz$ as shown in the figure. The speed in the frequency (highest frequency lowest frequency) is thus $320\ Hz$. The speed of sound in still air is $340\ m/s$.
You are provided with three similar, but slightly different, tuning forks, when A and B are both struck, a beat frequency of $f_{AB}$ is heard. When A and C are both struck, beat frequency of $f_{AC}$ is heard. It was noticed that $f_{AB} < f_{AC}$. This experiment is repeated after coating tuning fork A with a little wax. Now it is observed that values of both $f_{AB}$ and $f_{AC}$ increase.
The figure represents the instantaneous displacement-position graph of a longitudinal harmonic wave travelling along the negative x-axis, Identify the correct statement(s) related to the movement of the points shown in the figure.
You have designed a new musical instrument of very simple construction. Your design consists of a metal tube with length $l$ and diameter $\displaystyle\frac{l}{10}$. You have stretched a string of mass per unit length $\mu$ across the open end of the tube. The other end of the tube is closed. To produce the musical effect you are looking for, you want the frequency of the third harmonic standing wave on the string to be same as the fundamental frequency for sound waves in the air column in tube. Velocity of sound in the air column is $v$.
Dolphins emit high frequency sound waves typically $10^5\space Hz$ and use the echos for guidance and for hunting. The corresponding wave length in water is $1.48\space cm$ with this sonar system they can sense objects as small as (roughly) the wavelength. Ultrasonic imaging is a medical technique that uses exactly the same physical principle, sound waves of very short wavelength (or high frequency) called ultrasound are scanned over the human body the echos from the interior organs are used to create image. Ultrasound is more sensitive than x-rays in distinguishing various kinds of tissues and does not have the radiation hazards associated with the x-rays. Ultra sound is used for the study of heart valve action, detection of tumors and prenatal tests.