Processing math: 100%

User interface language: English | Español

Date May 2016 Marks available 3 Reference code 16M.2.HL.TZ0.4
Level Higher level Paper Paper 2 Time zone Time zone 0
Command term Demonstrate and Describe Question number 4 Adapted from N/A

Question

A longitudinal wave is travelling in a medium from left to right. The graph shows the variation with distance x of the displacement y of the particles in the medium. The solid line and the dotted line show the displacement at t=0 and t=0.882 ms, respectively.

The period of the wave is greater than 0.882 ms. A displacement to the right of the equilibrium position is positive.

(i) Calculate the speed of this wave.

(ii) Show that the angular frequency of oscillations of a particle in the medium is ω=1.3×103rads−1.

[4]
b.

One particle in the medium has its equilibrium position at x=1.00 m.

(i) State and explain the direction of motion for this particle at t=0.

(ii) Show that the speed of this particle at t=0.882 ms is 4.9ms−1.

[4]
c.

The travelling wave in (b) is directed at the open end of a tube of length 1.20 m. The other end of the tube is closed.

(i) Describe how a standing wave is formed.

(ii) Demonstrate, using a calculation, that a standing wave will be established in this tube.

[3]
d.

Markscheme

(i)
ALTERNATIVE 1
«distance travelled by wave =» 0.30 m 
v=≪distancetime=≫340ms1

ALTERNATIVE 2
evaluates T=0.882×103×1.60.3«=4.7ms» to give f = 210 or 212 Hz

uses λ=1.6 m with v= to give 340ms–1 

(ii)
ALTERNATIVE 1
λ=1.60m 
ω=≪2πf=≫2π×3401.60=1.3×103 or 1.34×103rads–1

ALTERNATIVE 2

«0.882 ms is 0.31.6 of cycle so whole cycle is» 2π×316×0.882×103
1.35×103rads–1

Allow ECF from (b)(i).

b.

(i)
the displacement of the particle decreases OR «on the graph» displacement is going in a negative direction OR on the graph the particle goes down OR on the graph displacement moves towards equilibrium/0

to the left 

Do not allow “moving downwards”.

(ii)
y=–1.5mm

v=2π×212×(4.0×103)2(1.5×103)2

«v=4.939≈4.9ms-1»

Allow ECF from (b)(ii).

Do not allow 4.3mm0.882ms=4.87ms1.

c.

(i)
the superposition/interference of two oppositely moving/reflected «identical travelling» waves

(ii)
the allowed wavelengths in the tube are λ=4Ln=480n, n = 1, 3, 5,…

OR

diagram showing 34 of a standing wavelength in the tube 

1.6=4.80nn=3

OR

justification that 34×1.6=1.2m

Allow diagram showing 34 of a wavelength for MP1.

d.

Examiners report

[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Core » Topic 4: Waves » 4.5 – Standing waves
Show 61 related questions

View options