# Physics 9702 Doubts | Help Page 123

__Question 621: [Waves > Stationary waves]__**(a)**State two features of stationary wave that distinguish it from a progressive wave

**(b)**Long tube is open at one end. It is closed at other end by means of a piston that can be moved along the tube, as shown Fig.1.

Loudspeaker producing sound of
frequency 550Hz is held near the open end of tube.

Piston is moved along the tube and a
loud sound is heard when the distance L between piston and open end of tube is
45cm. Speed of sound in tube = 330ms

^{-1}.
(i) Show that wavelength of the
sound in the tube is 60cm

(ii) On Fig.1, mark all positions
along the tube of:

1. Displacement nodes (label with
letter N)

2. Displacement antinodes (label
letter A)

**(c)**Frequency of the sound produced by loudspeaker in (b) is gradually reduced.

Determine lowest frequency at which
a loud sound will be produced in the tube of length L = 45cm

**Reference:**

*Past Exam Paper – June 2010 Paper 22 Q4*

__Solution 621:__**(a)**Choose any 2:

No energy transfer

The amplitude varies along its
length / nodes

__and__antinodes
The neighboring points (in an
inter-nodal loop) vibrate in phase, etc.

**(b)**

(i)

(v = fλ)

Wavelength λ = v / f = 330 / 550 =
0.6m = 60cm

(ii) 1. & 2.

A node labeled at the piston and antinode
labeled at the open end of the tube. Additional node and antinode in correct
positions along tube.

{The length L represent ¾
of a wavelength (45 / 60 = ¾ ) because there must be an antinode at the open
end and a node at the piston. I think that at 100%, L = 9cm (measured using a
ruler). The other antinode should be found at ¼ wavelength from the piston.
This is 9 / 3 = 3cm from the piston. The other node is at ½ wavelength, that is
a distance 2x3 = 6cm from the piston.}

**(c)**

At lowest frequency, length of tube
corresponds to λ /4

So, λ = 4x45 = 180cm = 1.8m

Frequency = (v/ λ =) 330 / 1.8 =
180Hz

__Question 622: [Current of Electricity > Resistance]__
Resistance of a metal cube is
measured by placing it between two parallel plates, as shown.

Cube has volume V and is made of a
material with resistivity ρ. Connections to the cube have negligible
resistance.

Which expression gives electrical
resistance of the metal cube between X and Y?

A ρV

^{1/3}B ρV^{2/3}C ρ / V^{1/3}D ρ / V^{2/3}**Reference:**

*Past Exam Paper – June 2011 Paper 13 Q35*

__Solution 622:__**Answer: C.**

Resistance R of a wire = ρL / A

Where L is the length of the wire
and A is the cross-sectional area of the wire.

For a cube, all the sides are of
equal lengths. Let the length be L/

Volume V = L

^{3}
Length = L and cross-sectional area
(in contact with the plates) = L

^{2}
Resistance R = ρL / L

^{2}= ρ / L
But since V = L

^{3}, length L = V^{1/3}
Resistance R = ρ / V

^{1/3}
Alternatively, if we consider the
units of the quantities involved, only choice C gives the unit of resistance (Ω).

Unit of resistivity = Ωm

Unit of volume V = m

^{3}
Unit of ρ / V

^{1/3}= [Ωm] / [m^{3}]^{1/3}= [Ωm] / m = Ω

__Question 623: [Quantum Physics]__**(a)**State an effect, one in each case, that provides evidence for

(i) wave nature of a particle

(ii) particulate nature of
electromagnetic radiation

**(b)**Four electron energy levels in an atom shown in Fig.1.

An emission spectrum is associated
with electron transitions between these energy levels.

For spectrum

(i) state number of lines

(ii) calculate minimum wavelength

**Reference:**

*Past Exam Paper – November 2010 Paper 41 & 42 Q7*

__Solution 623:__**(a)**

(i) e.g. electron / particle
diffraction

(ii) Photoelectric effect

**(b)**

(i) Number of lines: 6

{The question did not ask
for visible lines only. So, we include all the lines even if they are outside
the visible range.}

(ii)

(Emission spectrum is due
to transition from higher energy level to lower one)

(Energy E = hf = hc / λ. So the wavelength is minimum when
the change in energy is biggest.)

Change in energy (= [-0.87x10

^{-19}] – [-5.44x10^{-19}]) = 4.57x10^{-19}J
Wavelength λ = hc / E = [(6.63x10

^{-34})(3.0x10^{8})] / (4.57x10^{-19}) = 4.4x10^{-7}m

__Question 624: [Graphs]__**(a)**On axes of Fig.1, sketch variation with distance from a point mass of the gravitational field strength due to the mass.

**(b)**On axes of Fig.2, sketch variation with speed of the magnitude of the force on a charged particle moving at right-angles to a uniform magnetic field.

**(c)**On axes of Fig.3, sketch variation with time of the power dissipated in a resistor by a sinusoidal alternating current during two cycles of the current.

**Reference:**

*Past Exam Paper – November 2014 Paper 43 Q2*

__Solution 624:__**(a)**

{Gravitational field strength,
g = GM / x

^{2}}
The graph is a smooth curve with
decreasing gradient, not starting at x = 0.

{At zero distance from the
point mass, the gravitational field strength is infinite.}

The end of the line should not be not
at g = 0 or horizontal. {The gradient is not zero.}

**(b)**

{F = Bqv. The force F
depends linearly on the speed v. Charge q and magnetic field B are constant.}

The graph is a straight line with
positive gradient. The line starts at the origin.

**(c)**

{Power P dissipated = I

^{2}R. An alternating current is used, so the current can be described as varying sinusoidally. I = I_{0}sin(ωt).
However, in the formula,
we take the square of the current. So, all the negative values would become
positive – that is, the graph is a sin

^{2}curve.}
The graph has a sinusoidal shape
with only positive values and peak / trough are at height constant. At least, 4
‘loops’ should be shown.

__Question 625: [Waves > Interference > Double Slit]__
Diagram shows a view from above of
double slit interference demonstration.

L is monochromatic light source with
a vertical filament. B is a barrier with two narrow vertical slits and S is
screen upon which interference fringes form.

Intensity is I at a point on the
screen where centre of the fringe pattern forms.

What is the intensity, at the same
point, when one of the slits is covered up?

A I / √2 B I / 2 C I / 2√2 D I / 4

**Reference:**

*Past Exam Paper – November 2011 Paper 11 Q28 & Paper 13 Q27*

__Solution 625:__**Answer: D.**

At the central fringe, constructive
interference occurs, i.e. the resultant displacement is the sum of
displacements of each wave (here there is 2 waves due to the 2 slits).

By covering up one slit, the wave
amplitude is halved because only 1 wave is reaching that point.

Since intensity is proportional to
(amplitude)

^{2}, the intensity is one-quarter of the original intensity when the amplitude is halved..
For solution 624(c)

ReplyDeleteShouldn't the graph be of the form

1/2 (1-cos2x)?

[Since cos2x= 1-2sin^2x]

We only have to square the graph of sin. There is now no negative values.

DeleteCould you please explain solution 621 (c)? Why is it that at lowest frequency,length is wavelength/4? Thano you.

ReplyDeleteA node will always be present at the tube and an antinode at the open end of the tube.

DeleteThe lowest frequency simply corresponds to the (part of the) wave formed by directly joining the node (at the piston) and antinode (at the open end).

This is seen to represent a quarter of a wave. T

Thus, the length of the tube is equal to wavelength/4

Delete