C4: Standing waves and resonance

Question 1

What are nodes and antinodes

Answer 1

Nodes: Points that always show no displacement
Antinodes: Points that reach maximum amplitude of displacement are called antinodes

Question 2

What are the boundary conditions for standing waves to occur

Answer 2

When both ends of the vibrating string are fixed, such that each end is a node

Question 3

What is the frequency of each harmonic wave in a string or open pipe

Answer 3

f = nf1
n is the nth harmonic
f1 is the frequency of the first harmonic

Question 4

What is the wavelength of each harmonic wave in a string or open pipe

Answer 4

λ = (2L)/n
n is the nth harmonic

Question 5

What is the frequency of each harmonic wave in a closed pipe

Answer 5

f = nf1
n = 1, 3, 5…
f1 is the frequency of the first harmonic

Question 6

What is the wavelength of each harmonic wave in a closed pipe

Answer 6

λ = (4L)/n
n = 1, 3, 5…

Question 7

What is the comparison between the amplitudes in a stationary and travelling wave

Answer 7

Stationary wave:
All points on the wave have different amplitudes

Travelling wave:
All points on the wave have the same amplitude

Question 8

What is the comparison in energy in a stationary and travelling wave

Answer 8

Stationary wave:
Energy is not transmitted by the wave, but it does have an energy associated with it

Travelling wave:
Energy is transmitted by the wave

Question 9

What is the comparison in wave pattern in a stationary and travelling wave

Answer 9

Stationary wave:
Wave pattern does not move

Travelling wave:
Wave pattern moves

Question 10

What is the comparison of frequency in wave pattern in a stationary and travelling wave

Answer 10

Stationary and travelling wave:
All points oscillate with the same frequency

Question 11

How is wavelength calculated in a stationary and travelling wave

Answer 11

Stationary wave:
Twice the distance from one node (or antinode) to the next node (or antinode)

Travelling wave:
Shortest distance along the wave between two points that are in phase with one another

Question 12

What is the comparison of phase in wave pattern in a stationary and travelling wave

Answer 12

Stationary wave:
The phase of all points between two nodes are identical

Travelling wave:
All particles along a wavelength have different phases

Question 13

How does resonance occur

Answer 13

Resonance occurs when the resulting amplitude of the system becomes a maximum when the driving frequency of external driving force equals to natural frequency of the system

Question 14

What is damping

Answer 14

Process where energy is taken from an oscillating system as a result of dissipative forces

Question 15

What happens as the degree of damping is increased

Answer 15

The amplitude of the peak oscillation decreases
The peak becomes broader as it spreads over a wider range of frequencies
Resonance occurs at a frequency smaller than the natural frequency

Question 16

What happens during light damping

Answer 16

Oscillations are maintained about the equilibrium position after the system has been displaced and the amplitude of oscillations decreases over a long time

Question 17

What happens during critical damping

Answer 17

No oscillations occur as the motion is brought to rest in the shortest time possible

Question 18

What happens during heavy damping

Answer 18

No oscillations occur about the equilibrium position. Damping force increases beyond the point of critical dampung