standing waves vs beats

a standing wave in a string of length L (fixed at both ends) is produced when

• two travelling waves, travelling in the same direction and with the same frequency, superimpose.

• two travelling waves, travelling in the same direction and with the similar frequencies, superimpose so long as L = a multiple of λ/2 .

• two travelling waves, travelling in opposite directions and with the same frequency, superimpose.

• two travelling waves, travelling in opposite directions and with the same frequency, superimpose so long as L = a multiple of λ/2

a beating wave is produced when

• two travelling waves, travelling in the same direction and with the same frequency, superimpose.

• two travelling waves, travelling in the same direction and with the similar frequencies, superimpose

• two travelling waves, travelling in opposite directions and with the same frequency, superimpose.

• two travelling waves travelling in the same direction of the same frequency but of different amplitudes that superimpose

A standing wave can be described as

• a wave where the particles do not move

• a wave where all particles in the wave move the same amplitude but are all out of phase with each other

• a wave where all particles in the wave move with different amplitudes but they are all in phase with each other

• a wave where all particles in the wave move with different amplitudes and are all out of phase with each other

A beating wave can be described as

• a wave where all particles along the wave move with changing amplitudes over time and are all slightly out of phase with each other

• a wave where all particles along the wave move with the same amplitude but are all slightly out of phase with each other

• a wave where all particles in the wave move with different amplitudes but they are all in phase with each other

• a wave where all particles in the wave move with changing amplitudes over time but are all in phase with each other

What is the phase difference between two successive nodes in a standing wave?

• 45 degrees

• 90 degrees

• 180 degrees

• 0 degrees

What is the phase difference between a node and the successive (the next) antinode

• 45 degrees

• 90 degrees

• 180 degrees

• 0 degrees

the equation for all the possible wavelengths that can form in a standing wave in a length of string between two fixed ends is

• = 2L/n

• = 2n/L

• =n/2L

• = L/2n

what is the equation for the possible frequencies in a pipe open at both ends in terms of wave speed v

• 2n/vL

• 2L/nv

• nL/2v

• nv/2L

what are the differences between standing waves in a vibrating string and standing waves of air in a pipe

• The air particles move faster than particles in the string and move parallel to the pipe whereas the particles in the string move perpendicular to the length of the string. Nodes form at the open ends of the pipe but antinodes form at the ends of the string

• The air particles move slower than particles in the string and move parallel to the pipe whereas the particles in the string move perpendicular to the length of the string. Nodes form at the open ends of the pipe but antinodes form at the ends of the string

• The air particles move faster than particles in the string and move parallel to the pipe whereas the particles in the string move perpendicular to the length of the string. Antinodes form at the open ends of the pipe but nodes form at the ends of the string

• The air particles move slower than particles in the string and move parallel to the pipe whereas the particles in the string move perpendicular to the length of the string. Antinodes form at the open ends of the pipe but nodes form at the ends of the string

How are standing waves formed in a pipe with two open ends

• a longitudinal wave travels the length of the pipe and reflects at the open end, in phase. This means the reflected wave and original wave will add constructively forming a node. A quarter wavelength inside the pipe, the reflected wave is 90 degrees ahead of the particles at the open end and the original wave is 90 degrees behind the particles at the open end. This means the particles are 180 degrees out of phase with each other compared to the open end (where there is zero degrees phase difference). This means they must cancel each other and form an antinode. If the other open end is a quarter wavelength from the node then the waves are in phase again and another node will form. So long as the length of the pipe is a multiple of half wavelengths, then a standing wave will fit in it, with nodes at the open ends.

• a longitudinal wave travels the length of the pipe and reflects at the open end, in phase. This means the reflected wave and original wave will add constructively forming an antinode. A quarter wavelength inside the pipe, the reflected wave is 90 degrees ahead of the particles at the open end and the original wave is 90 degrees behind the particles at the open end. This means the particles are 180 degrees out of phase with each other compared to the open end (where there is zero degrees phase difference). This means they must cancel each other and form a node. if the other open end is a quarter wavelength from the node then another antinode will form. So long as the length of the pipe is a multiple of half wavelengths, then a standing wave will fit in it, with antinodes at the open ends.

• a longitudinal wave travels the length of the pipe and reflects at the open end, in phase. This means the reflected wave and original wave will add constructively forming an antinode. A half wavelength inside the pipe, the reflected wave is 90 degrees ahead of the particles at the open end and the original wave is 90 degrees behind the particles at the open end. This means the particles are 180 degrees out of phase with each other compared to the open end (where there is zero degrees phase difference). This means they must cancel each other and form a node. if the other open end is a half wavelength from the node then another antinode will form. So long as the length of the pipe is a multiple of half wavelengths, then a standing wave will fit in it, with antinodes at the open ends.