4.5 Stationary and progressive waves

Question 1

What is the first harmonic of the string?

Answer 1

» Also referred to as the fundamental mode of vibration, consists of a single loop that vibrates from side to side

Question 2

What is a node?

Answer 2

» A point of no diplacement
» Where destructive interference happens

Question 3

What is the antinode?

Answer 3

» The position in which the string vibrates with a maximum amplitude
» Where constructive interference happens

Question 4

What is the requirement for the first harmonic vibration to occur?

Answer 4

» The distance between the adjacent nodes must be half the wavelength

Question 5

What happens if the frequency of the waves steadily along the rope from each end is increased?

Answer 5

» New pattern is observed, looks like a transverse wave
» 3 nodes, one at the beginning, one at the end and one at the centre
» Only formed when frequency is twice as high as first harmonic vibration

Question 6

What is the length of the rope equal to in the wave which has a higher frequency then the first harmonic vibration?

Answer 6

» Equal to the wavelength, as the frequency is twice as high when compared to the first harmonic vibration

Question 7

What is one key fact about stationary waves that vibrate freely?

Answer 7

» Do not transfer energy to their surroundings

Question 8

How do stationary waves which move freely do not transfer energy to the surroundings?

Answer 8

» No energy at the nodes as amplitude is 0
» Amplitude of vibration at the antinodes is maximum
» So there is a maximum energy at antinodes
» However, they are at fixed positons, so no energy is transferred in a freely vibrating stationary wave pattern

Question 9

What happens when 2 progressive waves are in phase which other?

Answer 9

» They reinforce each other to produce a larger wave

Question 10

What is the phase difference between 2 particles?

Answer 10

» 0 if the 2 particles are between 2 adjecent nodes or even number of nodes
» 180, pie radians if the 2 particles are seperated by an odd number of nodes

Question 11

What is the differency in frequency between progressive waves and stationary waves?

Answer 11

» All particles except those at the nodes vibrate at the same frequency in a stationary wave
» All particles vibrate at the same frequency in a progressive wave

Question 12

What is the difference in amplitude between a stationary wave and a progressive wave?

Answer 12

» Amplitude varies from zero at the nodes to a maximum at the antinodes in a stationary wave
» Amplitude is the same for all particles in a progressive wave

Question 13

What is the difference in the phase difference of a stationary wave and a progressive wave?

Answer 13

» Phase difference is equal to mpie, where m is the number of nodes between the 2 particles
» In progressive waves, it is equal to 2pie x (D/wavelength) where d is the distance apart

Question 14

What happens to a point on a wave during a period?

Answer 14

» Moves to a maximum negative/positive displacement
» Returns to equilibrium position if it was previously there

Question 15

What is the 2nd harmonic known as?

Answer 15

» 1st overtone

Question 16

What is the 3rd harmonic known as?

Answer 16

» 2nd overtone

Question 17

What can stationary waves only be in?

Answer 17

» Phase or antiphase
» Phase difference of 180 degrees or 0

Question 18

What are the three things to increase the pitch of the first harmonic on the string?

Answer 18

» Decrease mass per unit length
» Decrease the length
» Increase the tension