KCL Section 3: Standing waves (Waves and Photons)

Question 1

Features of a standing waves?

Answer 1

The wave profile does not move - it appears to be stationary. Nodes have zero displacement, whereas antinodes reach max displacement.

Question 2

How is a standing wave formed?

Answer 2

This comes from continuous superposition of two waves which have:
the same frequency
the same speed
the same amplitude
a constant phase relationship
and are travelling in opposite directions.

Question 3

Define Standing wave:

Answer 3

no (net) transfer of energy OR pattern of nodes and antinodes OR points of maximum displacement and zero displacement

Question 4

Define Standing wave: (2)

Answer 4

Waves of same frequency/wavelength travel in both directions along wire and are reflected (not bounced). Superposition occurs producing nodes (destructive interference due to antiphase) and antinodes (constructive interference, in phase).

Question 5

What happens when a wave is reflected from a fixed point

Answer 5

When a wave is reflected from a fixed point there is a phase change of π rad (180o).
Destructive interference will occur at the point of reflection: given that this point will always be in antiphase it will become a node.

Question 6

How can a wave be standing?

Answer 6

If the wavelength of the reflected wave can fit the relationship nλ = 2L, where n is an integer, then a standing wave will be set up.

Question 7

A guitar wing of length 65cm vibrates in its fundamental mode. The speed of waves in the string is 362 ms^-1. What are the wavelength and frequency of this standing wave.

Answer 7

278 Hz

Question 8

A violin string of length 58 cm vibrates in the first harmonic, at a speed of 351 ms-1.
Give the wavelength of the wave
Calculate the frequency of the wave

Answer 8

1.16 m

303 Hz

Question 9

A violin string of length 61 cm vibrates in the second harmonic, at a speed of 346 ms-1.
Give the wavelength of the wave
Calculate the frequency of the wave

Answer 9

0.61 m

567 Hz

Question 10

A piano string of length 1.03 m vibrates in the third harmonic, at a speed of 505 ms-1.
Give the wavelength of the wave
Calculate the frequency of the wave

Answer 10

0.69 m

735 Hz

Question 11

What do the symbols mean?

v = √(T/μ)

Answer 11

v = wave speed
T = tension of the string
μ = mass per unit length of the string

Question 12

How fast do waves travel on a string held under a tension of 80 N, with a mass per unit length of 3.5 x 10-4 kgm-1?

Answer 12

478 ms-1

Question 13

How fast do waves travel on a string held under a tension of 140 N, with a mass per unit length of 8.9 x 10-4 kgm-1?

Answer 13

397 ms-1

Question 14

How fast do waves travel on a string held under a tension of 93 N, with a mass per unit length of 0.0010 kgm-1? 305 ms-1

Answer 14

305 ms-1

Question 15

How fast do waves travel on a string hung with a 45 N weight, with a mass per unit length of 1.42 x 10-3 kgm-1? 178 ms-1

Answer 15

178 ms-1

Question 16

How fast do waves travel on a string hung with two 9.8 N weights, with a mass per unit length of 2.0 gm-1?

Answer 16

99 ms-1

Question 17

How fast do waves travel on a string hung with a 500 g mass, with a mass per unit length of 0.78 gm-1?

Answer 17

79 ms-1

Question 18

How fast do waves travel on a string hung with six 20 g masses, with a mass per unit length of 6.70 x 10-4 kgm-1?

Answer 18

42 ms-1

Question 19

How fast do waves travel in a string that is held under 75 N tension and has a mass per unit length of 5.0 x 10-4 kg m-1? What would be its fundamental frequency if the string was 75.5 cm long?

Answer 19

256Hz

Question 20

How does reflection from fixed and open ends differ?

Answer 20

When reflection from a fixed end occurs the wave flips into antiphase. When reflection from an open end occurs the wave is reflected back.