IB Physics HL C Wave Behaviour Questions

Practise IB Physics HL wave behaviour through shared-core and HL resonance, interference, diffraction and standing-wave problems using measured data.

Exam points

Solve SHM, wave propagation and Doppler equations in multi-step problems with explicit phase, direction and initial conditions.
Derive or apply interference, diffraction, standing-wave, resonance and boundary conditions for extended HL evidence.
Evaluate wave energy transfer, experimental uncertainty, damping and frequency-shift models using HL data.

Covered syllabus points

C.1 Simple harmonic motion C.2 Wave model C.3 Wave phenomena C.4 Standing waves and resonance C.5 Doppler effect

[Maximum number: 13]

(a)

One end of a light spring is attached to a rigid horizontal support.

An object W of mass 0.15 kg is suspended from the other end of the spring. The extension x of the spring is proportional to the force F causing the extension. The force per unit extension of the spring k is $18 \mathrm{Nm}^{-1}$ .

A student pulls W down such that the extension of the spring increases by 0.040 m . The student releases W and as a result W performs simple harmonic motion (SHM).

[ 5 ]

(i)

State what is meant by the expression "W performs SHM".

[ 2 ]

(ii)

Determine the period of oscillation of the spring.

[ 3 ]

$\omega=\sqrt{\frac{a}{x}}$ ;
$=10.95 \mathrm{~rad} \mathrm{~s}^{-2}$ ;
$T=\left(\frac{2\pi}{\omega}=\right) \frac{6.28}{10.95}=0.57 \mathrm{~s}$ ;

(b)

W in (a) is immersed in a beaker of oil. As a result of this immersion the oscillations of W are critically damped. Describe what is meant by critically damped.

[ 2 ]

(c)

A spring, such as that in (a), is stretched horizontally and a longitudinal travelling wave is set up in the spring, travelling to the right.

[ 6 ]

(i)

Describe, in terms of the propagation of energy, what is meant by a longitudinal travelling wave.

[ 2 ]

(ii)

The graph shows how the displacement x of one coil C of the spring varies with time t.

Figure for Question (ii) — IB Physics HL

The speed of the wave is $3.0 \mathrm{~cm} \mathrm{~s}^{-1}$ . Determine the wavelength of the wave.

[ 2 ]

frequency $=\left(\frac{1}{T}=\frac{1}{0.80}=\right) 1.25 \mathrm{~Hz}$ ;
wavelength $=\frac{v}{f}=\frac{3.0}{1.25}=2.4 \mathrm{~cm}$ or $2.4 \times 10^{-2} \mathrm{~m}$ ;

(iii)

Draw, on the graph in (c)(ii), the displacement of a coil of the spring that is 1.8 cm away from C in the direction of travel of the wave, explaining your answer.

[ 2 ]

[Maximum number: 15]

(a)

Outline what is meant by a travelling wave.

[ 2 ]

(b)

A loudspeaker emits sound of frequency 210 Hz into a pipe with one open and one closed end. The diagram shows a representation of the standing wave established in the pipe.

The length of the pipe is 1.20 m .

[ 5 ]

(i)

Outline how the standing wave is formed in the pipe.

[ 2 ]

(ii)

Determine the wavelength of the wave.

[ 1 ]

$\lambda=\lessdot \frac{4 L}{3}=\frac{4 \times 1.20}{3}=>1.6<\mathrm{m} \gg$

(iii)

Calculate the speed of sound in the pipe stating the answer to an appropriate number of significant figures.

[ 2 ]

$c=\lambda f=1.60 \times 210=336$ OR $340\ \mathrm{m}\ \mathrm{s}^{-1}$
Any answer to 2 OR 3 s.f.

Marking guidance:

Allow ECF from incorrect wavelength in bii)

(c)

The solid line represents the standing wave at time t and the dotted line represents the standing wave at an instant later. The dot is the equilibrium position of a particle P in the pipe. The up arrow indicates displacements to the right and the down arrow displacements to the left.

On the diagram, draw

[ 2 ]

(i)

a dot to indicate the approximate position of P at time t,

[ 1 ]

(ii)

an arrow to indicate the velocity of P at time t.

[ 1 ]

(d)

The amplitude of oscillations of the standing wave in (b) is 4.2 mm . The mass of particle P in (c) is $1.8 \times 10^{-6} \mathrm{~kg}$ .
Calculate

[ 4 ]

(i)

the total energy of P,

[ 2 ]

$\begin{aligned} \omega=\ll 2 \pi f \Rightarrow 2 \pi \times 210=1.319 \times 10^{3} \ll \mathrm{rad} \mathrm{~s}^{-1} \gg \quad \ll \operatorname{Energy}=\frac{1}{2} m \omega^{2} x_{o}^{2}=\frac{1}{2} \times 1.8 \times 10^{-6} \times\left(1.319 \times 10^{3}\right)^{2} \times\left(4.2 \times 10^{-3}\right)^{2}=\gg \end{aligned}$

MP1 can be awarded for a
correct substitution or value

[2]

$2.7 \times 10^{-5}$ OR $2.8 \times 10^{-5} \ll \mathrm{~J} \gg$

(ii)

the displacement of P , when its kinetic energy is equal to its potential energy.

[ 2 ]

ALTERNATE 1
$\begin{aligned} & \frac{1}{2} m \omega^{2} x^{2}=\frac{1}{2} \times\left(\frac{1}{2} m \omega^{2} x_{0}^{2}\right)^{} & x=\frac{x_{0}}{\sqrt{2}}=\frac{4.2}{\sqrt{2}}=3.0 \text { «mm» } & \text { ALTERNATE } 2 & \frac{1}{2} m \omega^{2}\left(x_{0}^{2}-x^{2}\right)=\frac{1}{2} m \omega^{2} x^{2} & x=\frac{x_{0}}{\sqrt{2}}=\frac{4.2}{\sqrt{2}}=3.0 \text { «mm» } & \text { ALTERNATE } 3 \end{aligned}$

Recognition that potential energy is $1.4 \times 10^{-5} \ll \mathrm{~J}>$ $x=\pi \sqrt{\frac{2 \times 14 \times 10^{-3}}{1.8 \times 10^{-6} \times\left(1.33 \times 10^{3}\right)^{2}}}=>3.0<\mathrm{mm} \gg<$

For Alternate 3 allow ECF from the
energy value from di).

[2]

(e)

The frequency of sound is reduced to 140 Hz . Explain why a standing wave will not be formed in the pipe.

[ 2 ]

ALTERNATE 1

the pipe can only support standing waves with frequencies that are odd multiples of the first harmonic frequency

first harmonic frequency is $70 \mathrm{~Hz}$

ALTERNATE 2

<<the new wavelength would be 2.4 m so>> a node would be formed at the open end

An antinode is required at the open end to form a standing wave

[Maximum number: 2]

A converging lens is placed between an object and a screen. An image of the object is formed on the screen.

(a)

Draw a ray to locate the focal point of the lens. Label this point with the letter F .

[ 1 ]

(b)

The lens suffers from spherical aberration.

[ 1 ]

(i)

Draw lines to complete the rays in the diagram.

[ 1 ]

[Maximum number: 12]

Two loudspeakers, A and B, are driven in phase and with the same amplitude at a frequency of 850 Hz . Point P is located 22.5 m from A and 24.3 m from B. The speed of sound is $340 \mathrm{~ms}^{-1}$ .

(a)

Deduce that a minimum intensity of sound is heard at P.

[ 4 ]

wavelength $=\frac{340}{850}=0.40$ «m»

path difference =1.8 «m»

1.8 «m» $=4.5 \lambda$ OR $\frac{1.8}{0.20}=9$ «half-wavelengths»

waves meet in antiphase «at P»

OR

destructive interference/superposition «at P»

Marking guidance:

Allow approach where path length is calculated in terms of number of wavelengths;
along path A (56.25) and path B (60.75) for MP2, hence path difference 4.5 wavelengths for MP3

(b)

A microphone moves along the line from P to Q . P Q is normal to the line midway between the loudspeakers.

B 咧

The intensity of sound is detected by the microphone. Predict the variation of detected intensity as the microphone moves from P to Q.

[ 2 ]

(c)

When both loudspeakers are operating, the intensity of sound recorded at Q is $I_{0}$ . Loudspeaker B is now disconnected. Loudspeaker A continues to emit sound with unchanged amplitude and frequency. The intensity of sound recorded at Q changes to $I_{\mathrm{A}}$ .

Estimate $\frac{I_{\mathrm{A}}}{I_{0}}$ .

[ 2 ]

the amplitude of sound at Q is halved

«intensity is proportional to amplitude squared hence» $\frac{I_{A}}{I_{0}}=\frac{1}{4}$

(d)

In another experiment, loudspeaker A is stationary and emits sound with a frequency of 850 Hz . The microphone is moving directly away from the loudspeaker with a constant speed v. The frequency of sound recorded by the microphone is 845 Hz .

[ 4 ]

(i)

Explain why the frequency recorded by the microphone is lower than the frequency emitted by the loudspeaker.

[ 2 ]

(ii)

Calculate v.

[ 2 ]

$\begin{aligned} 845=850 \times \frac{340-v}{340} v=2.00<\mathrm{m} \mathrm{~s}^{-1}>- \end{aligned}$

All question bank results loaded

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (b)

Question (c)

Question (i)

Question (ii)

Question (iii)

Question 2

Question (a)

Question (b)

Question (i)

Question (ii)

Question (iii)

Question (c)

Question (i)

Question (ii)

Question (d)

Question (i)

Question (ii)

Question (e)

Question 3

Question (a)

Question (b)

Question (i)

Question 4

Question (a)

Question (b)

Question (c)

Question (d)

Question (i)

Question (ii)