Longitudinal Standing Waves

A parallel beam of light is incident on a tank filled with water up to a height of 61.5 mm as shown in the figure below. Ultrasonic waves of frequency 0.5 MHz are sent along the length of the water column using a transducer placed at the top, and they form longitudinal standing waves in the water. Which of the schematic plots below best describes the intensity distribution of the light as seen on the screen ? Take the speed of sound in water to be 1,500 m/s.

A longitudinal standing wave y = a cos kx cos omega t is maintained in a homogeneious medium of density rho . Here omega is the angular speed and k , the wave number and a is the amplitude of the standing wave . This standing wave exists all over a given region of space. The space density of the potential energy PE = E_(p)(x , t) at a point (x , t) in this space is

A longitudinal standing wave y = a cos kx cos omega t is maintained in a homogeneious medium of density rho . Here omega is the angular speed and k , the wave number and a is the amplitude of the standing wave . This standing wave exists all over a given region of space. The space density of the kinetic energy . KE = E_(k) ( x, t) at the point (x, t) is given by

A longitudinal standing wave y = a cos kx cos omega t is maintained in a homogeneious medium of density rho . Here omega is the angular speed and k , the wave number and a is the amplitude of the standing wave . This standing wave exists all over a given region of space. If a graph E ( = E_(p) + E_(k)) versus t , i.e., total space energy density verus time were drawn at the instants of time t = 0 and t = T//4 , between two successive nodes separated by distance lambda//2 which of the following graphs correctly shows the total energy (E) distribution at the two instants.

A longitudinal standing wave xi a cos kx. Cos omega t is maintained in a homogeneous medium of density rho . Find the expressions for the space density of (a) potential energy w_(p)(x,t), (b) kinetic energy w_(k)(x,t), Plot the space density distribution of the total energy w in the space between the displacement nodes at the moments t=0 and t=T//4 , where T is oscillation period.

The equation of a longitudinal standing wave due to superposition of the progressive waves producted by two sources of sound is s = -20 sin 10 pix sin 100 pit where s is the displacement from mean position measured in mm, x is in meters and is in seconds. The specific gravity of the medium is 10^(-3) . Density of water = 10^(3)kg//m^(3) . Find : (a) Wavelength, frequency and velocity of the progressive waves. (b) Bulk modulus of the medium and the pressure amplitude. (c) Minimum distance between pressure antinode and a displacement anotinode. (d) Intensity at the displacement nodes.

Sound travels in rocks in the form of both longitudinal and transverse waves, but in air, sound travels only in the form of longitudinal waves'. Explain

Distinguish between longitudinal and transverse waves.

In a longitudinal stationary waves, node is a point of