4.5 - Stationary Waves and Progressive Waves

Question 1

when is a stationary wave formed

Answer 1

when two progressive waves pass through eachother

this can be achieved when on a string if tension is fixed at both ends and the middle part vibrates so that the progressive waves travel towards each end, reflect at each end and then pass through eachother

Question 2

what is the fundamental mode of vibration also referred to as

Answer 2

the first harmonic

Question 3

what are the features of the first harmonic

Answer 3

A single loop
2 nodes (points of no displacement)
1 Antinode (maximum amplitude midway between the nodes)

Question 4

what distance between the adjacent nodes is needed to create a first harmonic

Answer 4

1/2 lambda

Question 5

what happens if you raise the frequency of the vibration to twice as high when it is at its first harmonic

Answer 5

to becomes the second harmonic

Question 6

features of the second harmonic

Answer 6

nodes at either end and one in the centre

2 antinodes

full wavelength

Question 7

what do stationary waves that vibrate freely not do

Answer 7

transfer energy to their surroundings but they do transfer matter

Question 8

why is no energy transferred in a stationary wave

Answer 8

the amplitude of vibration is zero at the nodes and amplitude of vibration is maximum at the antinodes

because the nodes and antinodes are fixed positions no energy is transferred in a freely vibrating stationary wave pattern

Question 9

what happens a quarter of a cycle after 2 progressive waves have combined to create a larger wave

Answer 9

each wave has moved one quarter of a wavelength in opposite directions and they are now in anti phase so cancel eachother out

after another quarter cycle the two waves are back in phase and create a larger wave again

Question 10

what happens to the amplitude of a vibrating particle in a stationary wave pattern

Answer 10

it varies from zero at the node to maximum amplitude at the antinode

Question 11

phase difference for particles in a stationary wave

Answer 11

zero if the two particles are between adjacent nodes or separated by an even number of nodes

180 or 1pi if the two particles are seperated by an odd number of nodes

Question 12

frequency difference in stationary and progressive waves

Answer 12

stationary

all the particles except those at the nodes vibrate at the same frequency

progressive

all particles vibrate at the same frequency

Question 13

amplitude difference in stationary and progressive waves

Answer 13

stationary

the amplitude varies from zero at the nodes to maximum at the antinodes

progressive

the amplitude is the same for all particles

Question 14

difference in phase difference between 2 particles in stationary and progressive

Answer 14

stationary

equal to m pi where m is the number of nodes between the two particles

progressive

equal to 2piD/lambda

Question 15

stationary waves sound in a pipe

Answer 15

sound resonates at certain frequencies in an air filled tube or pipe

in a pipe closed at one end these resonant frequencies frequencies occur when there is an antinode at the open end and and a node at the other end

Question 16

using microwaves to find the nodes of a stationary wave

Answer 16

microwaves transmitted at a metal plate normally and are reflected back toward the transmitter

when a detector id moved along the line between the transmitter and the metal plate

the detector signal is found to be zero at equally spaced positions along the line