Show that even as well as odd harmonics are present as overtone in modes of vibration of string

Show that even as well as odd (all) harmonics are present as overtones in the case of an air column vibrating in a pipe open at both ends.

Show that only odd harmonics are present in the vibrations of air column in a pipe closed at one end.

The harmonics produced in a vibrating string are

With neat diagram , explain various modes of vibration of a stretched string.

A string is fixed at the two ends and is vibrating in its fundamental mode. It is known that the two ends will ba at rest. A part from these, is there any position on the string ich can be touched so as not to disturb the motion of the string? What will be the answer to this question if the string is vibrating in its first and second overtones?

Prove that all harmonics are present in the vibrations of the air column in a pipe open at both ends.

A vibrating string of certain length l under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75cm inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n . Now when the tension of the string is slightly increased the number of beats reduces 2 per second. Assuming the velocity of sound in air to be 340 m//s , the frequency n of the tuning fork in Hz is

A string is stretched within two rigid ends. It is vibrated in a node of first overtone. Which of the following is formed at a middle point of a string ?

The velocity of a transverse wave on a string of length 0.5 is 225 m/s . While this string is vibrating in the fundamental harmonic , what is the wavelength of sound produced in air if the velocity of sound in air is 330 m/s ?