Draw a diagram to show The standing pressure wave and standing displacement wave for the 3rd overtone mode of vibration of an open organ pipe.

A string of length L fixed at both ends vibrates in its fundamental mode at a frequency v and a maximum amplitude A. (a) Find the wavelength and the wave number k. (b) Take the origin at one end of the string and the X-axis along the string. Take the Y-axis along the direction of the displacement. Take t = 0 at the instant when the middle point of the string passes through its mean position and is going towards the positive y-direction. Write the equation describing the standing wave.

A sound wave of wavelength 40 cm travels in air. If the difference between the maximum and minimum pressures at a given point is 1.0xx10^-3Nm^-2 , find the amplitude of vibration of the particle o the medium. The bulk modulus of air is 1.4xx10^5Nm^-2 .

An aluminium rod having a length of 90.0 cm is clamped at its middle point and is set into longitudinal vibrations by stroking it with a rosined cloth. Assume that the rod vibrates in its fundmental mode of vibration. The density of aluminium is 2600 kgm^-3 and its Young's modulus is 7.80xx10^10 Nm^-2 . Find a. The speed of sound in aluminium, b. The wavelength of sound waves produced in the rod. c. The frequency of the sound produced and d. The wavelength of the sound produced in air. Take the speed of sound in air to be 340 ms^-1 .

An air column is constructed by fitting a movable piston in along cylindrical tube. Longitudinal waves are sent in the tube by as tuning fork of frequency 416 Hz. How far from the open end should the piston, be so that the air column in the tube may vibrate in its first overtone? Speed of sound in air is 333ms^-1 .

A long string having a cross- sectional area 0.80 mm^2 and density 12.5 g cm^(-3) is subjected to a tension of 64 N along the X-axis. One end of this string is attached to a vibrator moving in transverse direction at a frequency fo 20Hz. At t = 0. the source is at a maximujm displacement y= 1.0 cm. (a) Write the equation for the wave. (b) What is the displacement of the particle of the string at x = 50 cm at time t = 0.05 s ? (c) What is the velocity of this particle at this instant ?

A 30.0-cm-long wire having a mass of 10.0 g is fixed at the two ends and is vibrated in its fundamental mode.A 50.0-cm-long closed organ pipe, placed with its open end near the wire, is set up into resonance in its fundamental mode by the vibrating wire. Find the tension in the wire. Speed of sound in air = 340 m s^-1 .

A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200 m s and the amplitude is 0.5 cm. (a) Find the wavelength and the frequency. (b) Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x= 50 cm has reached its maximum displacement.