Experimental Tasks: APhO 2022
Academic Committee: Chandan Ralekar, Siddhant Mukherjee,
Siddharth Tiwary, Charudutt Kadolkar, Bipul Pal, Manoj Harbola,Mamatha Maddur, Praveen Pathak
Acknowledgement: Chinmay Haritas, Shirish Pathare

APhO 2022

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EQ1: Magnetic Black box

Based on making use of various sensors available on a smartphone.

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Motivation

Hall effect based magnetic sensor to detect the magnetic field.

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May 263 / 18ExperimentBlackbox (magnet in a conducting pipe)

To identify different sections of the pipe with the help of a smartphone.

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Theoretical background

The axial magnetic field Bx of a point dipole (dipole moment M) at thedistance x
µ0 M
Bx =
2π x 3
When the magnet is moving with a constant non-relativistic velocity
Bx (t) =PP (HBCSE-TIFR)µ0 M
2πBx (t)µ0 M
2π (vt)3
1/3

APhO experiment= vtMay 26

5 / 18Three parts of the experiment:
Find the location of the magnetometer in the smartphone.
Determine the dipole moment M.
Determine v of the magnet.

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Simulation

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1. Find the location of the magnetometer
Bw
NBl

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2. Dipole moment of the magnet

Bw =µ0 M
2π x 3·10−3B (T)

3data
4.00 × 10−7 X + 3 × 10−62

10
2,000

4,0006,0008,0001(m−3 )
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3. Identify sections of the pipe
When the magnet is dropped in a non magnetic conducting pipe such asaluminium or copper; mÿ = mg − k ẏ
CD:Copper

6540.14

B
0.12

BC:Wood
0.11
0.1
0.09

0.6 0.7 0.8 0.9t (s)

1

1.1

0.08

A 0.070.1(2µ0 M/4πBw )1/3 (m)7DC

AB:Aluminum(2µ0 M/4πBw )1/3 (m)8·10−21.04

PP (HBCSE-TIFR)(2µ0 M/4πBw )1/3 (m)

0.16

1.06

1.08t (s)APhO experiment

1.1

1

1.5

2 2.5t (s)

33.5

1.12

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Length of each section

Identify the entry and exit time stamps in the data for each section anduse the obtained velocities to calculate the section lengths.

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EQ2: Accoustic Black box

Doppler effect in waves and an attempt to simulate acoustically the lightwaves emitted from the rotating planets.

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QuestionySvsSound source starts moving
at A and emits frequency f0 .
S is the position of the sourceat later time t.
You are given a detector D
which you can place or movein the x − y plane.
Find f0 , ω, R, vs , β,coordinates of A and C.

AϕC

BD

θ

βrD

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αx

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EQ2: Acoustic black box⃗ n̂
Detector’s velocity: vDVector DS:
Source’s net velocity: vTFrequency detected by the detector, when S is moving away (orapproaching) from Df (t ′ ) = f0c − ⃗vD · n̂(t)c ± ⃗vT · n̂(t)At large distance (or time)
SDSvT = vs − ωR

vT = vs − ωRvT = vs + ωR

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vT = vs + ωR

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Simulation

Change detector’s parameters

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Asymptotic limit
Detector position rD = 10000 m, θ = 35◦
f0 c(c−vs −ωR)SDS

f0 c(c−vs +ωR)

f0 c(c+vs −ωR)fmax +fminc−vsfmax −fmin = ωRf0 c(c+vs +ωR)
vs∆t = 2π
ω 1+ cfmax +fmin
c+vsfmax −fmin = ωR

Above three equations yield f0 , ω, R, f0 and vs .
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Source’s initial coordinates - Triangulation
Detector Location (rD , θ)(500,0)(0,500)(0,0)

PP (HBCSE-TIFR)First signal received (s)
1.535
1.273
1.979

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Summary

How to setup an experiment.
Observational and experimental skills, visualization, datainterpretation and analytical skills.

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