Hello Sound fans! Listen to Sydney!

Classical Mechanics Level 1

Suppose your friend lives in Sydney, Australia, and today the Indian Prime minister, Narendra Modi, is about to deliver a speech in the Opera House. Your friend has reserved a seat 20 meters from the microphone. You are listening to the same speech on the radio in Mumbai, roughly 10,000 km from Sydney.

Suppose the time it takes for the sound to reach you is $t_\textrm{radio}$ and the time it takes to reach your friend is $t_\textrm{live}$ . How much faster does the sound reach you, compared to your friend (i.e. find $t_\textrm{live}/t_\textrm{radio}$ )?

Details and Assumptions :

Take the speed of sound to be $300 \text{ m/s}$ .
The speed of radio waves is $300,000 \text{ km/s}$ .

Image Credit: Youtube Prime Minister Narendra Modi's Full Speech In Sydney, Australia .

The answer is 2.

7 solutions

Sravanth C.
Apr 29, 2015

Let's first jot down all the information.

Distance between your friend and Modi = $20$ m

Distance between you and Modi = $10,000$ km $= 10,000,000$ m $= 10^{7}$ m.

Speed of sound = $3×10^{2}$ m/s

Speed of radio waves = $3×10^{5}$ km/s $= 3×10^{8}$ m/s

We know that, $\text{speed} = \dfrac{\text{distance}}{\text{time}}$

Therefore, $\text{time} = \dfrac{\text{distance}}{\text{speed}}$

Hence, time taken by sound to reach your friend = $\dfrac{20}{3×10^{2}}$ $\hspace{1cm}$ (1)

Similarly time taken by sound to reach you = $\dfrac{10^{7}}{3×10^{8}}$ $\hspace{1cm}$ (2)

Therefore the ratio between (1) and (2) is, $\dfrac{\dfrac{20}{3×10^{2}}}{\dfrac{10^{7}}{3×10^{8}}}$

Or, $\dfrac{20}{3×10^{2}} × \dfrac{3×10^{8}}{10^{7}} = \dfrac{20}{10} = \boxed{2}$ .

Therefore, time taken by sound waves is twice the time taken by radio waves.

Hence, the sound will reach you 2 times faster! It sounds impossible, but it is possible. . .

But there are two electronic processing delays, not just transmission time involved , and you do not sit right on top of your radio....daft question!

Carol Blyth - 5 years, 7 months ago

This problem is misleading!

A Former Brilliant Member - 3 years, 4 months ago

This problem is very misleading indeed, I was going to mention the modulation and demodulation processes but I forgot that you might even be far from the radio! Good point

Glenn Renner - 2 years, 2 months ago

The expression "twice as fast" does not have the same meaning as the expression"two times faster." You need to be precise on this. A is x times greater/faster/ than B means A=x*B+B=(x+1)B

Shengyuan Chen - 5 years, 1 month ago

Yeah, Really does Sound Impossible :P

Mehul Arora - 6 years, 1 month ago

I did the same.Good question!

Siddharth Singh - 6 years, 1 month ago

Thanks! Hope you enjoyed it. $\huge \ddot\smile$

Sravanth C. - 6 years, 1 month ago

The question also does not take into account how far you are from the speaker on the radio or television. If you are 10 meters away, the sound would reach both listeners at approximately the same time.

Steve Popoff - 4 years, 11 months ago

Not to mention the fact that most radio stations are on a time delay of at least a few seconds to begin with. Impossible and poorly written question. =P Voice Over Actor

Rob Pigoni - 4 years, 11 months ago

It seems like many questions in Brilliant are worded incorrectly or have flawed logic.

Manuel Espinosa - 1 year, 5 months ago

Is sounds impossible, and in practically, its really impossible. Because there's Signal Attenuation, Broadcasting Delay etc. And that's why you see your friend in Mumbai celebrating the 6 in IPL, and you join him a bit later , as you're seeing the match in your TV.

Your concept is brilliant.

Muhammad Arifur Rahman - 6 years, 1 month ago

by far, most of the delay will be induced by satellite transmission !

Andrei Woinaroski - 5 years, 3 months ago

Thank you very much! Hope you enjoyed solving it.

Sravanth C. - 6 years, 1 month ago

Undoubtedly.

I didn't think before in such way. Anybody would be amazed.

Muhammad Arifur Rahman - 6 years, 1 month ago

@Muhammad Arifur Rahman – You're most welcome

Sravanth C. - 6 years, 1 month ago

The concept is extremely flawed, as it doesn't specify frequency, or propagation delay (ie. all radio waves move at the speed of light, but not the same distance as distance traveled for a radio wave is relative to it's frequency). Accounting for the exacting science of Special Relativity (if I remember it right), you both theoretically would hear the sound at the same time relative to physical position of the "observer" (yourself). It would be your perceptions of the sound that were skewed based upon distance traveled, and any external delays incurred.

Richard Smith - 5 years, 2 months ago

Dan Rumney
Dec 17, 2015

This is actually a poorly worded question. "Faster" implies velocity, and in this instance, the difference is a factor of 1000.

What the question is actually asking is about the ratio of the time taken for the signals (audio in one case, radio in another) to reach two different observers who are different distances away from the speaker.

In that instance, where the signal speed and the distance traveled are different, the signal reaches the Sydney observer in twice the time it takes to reach the Mumbai observer. However, it didn't get there faster. It got there sooner.

Thank you for finally agreeing with me on this. It's absolutely worded wrong. It should ask how many times sooner

Malachi Lingg - 4 years, 9 months ago

Would the answer differ depending on Modi's distance from the microphone?

A Former Brilliant Member - 4 years, 1 month ago

You're still wrong about it being 1000 times faster.

Everett Stuckless - 2 years, 10 months ago

Agreed. As an electrician I'd calculated each to the microsec based on the question, it reaches Mumbai guy 33.3 micro-seconds faster? Or did I implore poor math but still came out with twice as fast?

Jory Turgeon - 2 years, 8 months ago

Christopher Unrau
Nov 13, 2015

Your friend is 20m from the (implied) source of the sound. With sound travelling 300m/s, this means that the sound will reach him/her in 2/30 of a second. Normally you would simplify the fraction, but as I found out, it's simpler to leave it as is. You're 10,000 km away, and radio waves come at 300,000km/s. This takes 1/30 of a second. Meaning, you get it in 1/30 of a second, your friend in 2/30. 1/30*2 is 2/30 or 1/15, so you get it 2 times as fast.

I tried to 1/2, as in it takes half the time for the sound to reach you as it does you friend, but it didn't let me submit it, so I looked.

Jason Prometheus - 2 years, 5 months ago

Simple Algebra

Rilwan Ola-Dauda - 1 year, 9 months ago

Dartimos .
Jul 3, 2017

Given the processor time for microphone encoding and speaker decoding your friend probably hears it sooner.

Jonh Benjamin
Oct 18, 2016

Something is wrong here. The question is worded wrongly. "How much faster the sound reach you, compared to your friend (i.e. find tlive/tradio)?" Since tlive =0.6666seconds and tradio is 0.33333 seconds, it takes twice as long for the live transmission. So, the live transmission is not faster, it's slower.

Cecelia Naomi
Oct 30, 2015

How far is the listener from the radio?

Well that distance is neglected :)

Sravanth C. - 5 years, 7 months ago

Yeah, I don't get it. What happened to the transmission broadcast delay and also how far are you sitting from the radio?

Rassei Cox - 5 years, 1 month ago

Truong Quoc Bao
Jun 18, 2015

nice math problem I enjoy solving it i did the same way that u did but I solve this in the second try it sound kind of impossible but it's great

Thanks! ;)

Sravanth C. - 5 years, 7 months ago

Hello Sound fans! Listen to Sydney!

Image Credit: Youtube Prime Minister Narendra Modi's Full Speech In Sydney, Australia .

The answer is 2.

7 solutions

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