Could there be a mistake in the textbook solutions?

[nikstar]

I have Honors in Physics and am a qualified teacher, but I've taken 4 yrs out to have kids. I'm trying to get back into it by starting with tutoring, and I am totally perplexed by this solution to the question, so think there is a fault with it. The book is a new edition so it is possible. I'm going nuts that I can't solve it!

Homework Statement

If the speed of sound in air is 346ms^-1, at what speed would the sound from a fire truck siren appear to be traveling in the following situations?

a) You are driving towards the stationary fire truck at 30ms^-1

b)You are driving away from the stationary truck at 40m/s

c)You are stationary ant the fire truck is heading towards you at 20m/s

d)You are driving at 30m/s and about to overtake the fire truck, which is traveling at 20m/s in the same direction.

Homework Equations

i
None - it comes under the 'relativity' section and the student is not supposed to have studied the doppler effect yet, although there is a paragraph that stated, "If you are moving towards a source of sound, the speed of sound will be the sum of the speed of sound and your own speed"

The Attempt at a Solution

So (a) and (b) are easy to answer - 376m/s and 306m/s respectively, BUT (c) and (d) are beyond me!
(c) solution given is 346m/s - is that because "I" am stationary?
(d) solution given is 376m/s - it that because you only look that "I" am moving at 30m/s and you ignore the moving truck?

It just doesn't make any sense to me - esp when you take into account doppler effect. If anyone can explain it rather than just fudging the the explanation to fit the solutions I would be able to sleep much better!

 

[Filip Larsen]

The sound is pressure waves propagated in an air mass. Assuming the air is stationary, i.e. that all speeds in the problem text is relative to the air mass, you should think about if the speed of a sound reaching you depends on the speed of the source or not. Note, that the problem text only speaks of speed of sound, not frequency, so you don't need to know about the Doppler to solve these problems.

 

[nikstar]

It would appear that the source doesn't matter... but it should, shouldn't it?
I was just thinking that with the Doppler effect it is both the source and the object that matter... i.e. Frequency changes if either the source moves or you move, so I just thought it would be similar with the speed of the sound as v=f*wavelength...

 

[Borek]

It would appear that the source doesn't matter... but it should, shouldn't it?

Why? Speed of sound is property of the medium, not of the source.

 

[hikaru1221]

Hi,
Sound wave speed doesn't depend on the source; it only depends on the medium. The situation when the source moves will be like after it emits a wave front, the wave front and the source move as if they don't "know" each other. Therefore, in any cases, since the medium doesn't move at all, in the stationary reference frame, the wave speed is always 346m/s, which accounts for answers in (c) and (d).

 

[Filip Larsen]

A sound wave is small pressure disturbance in the air and such a disturbance propagate through the air with a speed that only depends on the characteristics of the air. Only if the source moved with speeds near or above the speed of sound would it be able to affect the parcels of air that the sound waves passes through. So, in the context of your problem, the speed of the source has no influence on the speed of the sound through the air.

The reason that the speed of the source then matters for frequency and wave length is because the distance between the waves (wave length) or the time between each wave passes a fixed spot in the air (frequency) depends on how far the source moves between sending one wave and the next. The usual visual model for waves is to imagine one wave being an expanding circle with the center where the wave was originally emitted. When the source stand still, successive waves will be concentric circles, but when it moves steadily in one direction the circles will not be concentric but tend to be closer to each other in the direction the source moves (shorter wavelength, higher frequency) and farther away in the other direction (longer wavelength, lower frequency).

 

[nikstar]

Nope. None of those solutions really help.

The solution states that the apparent speed of sound changes when the object moves.

Hikaru - if you note the answers for (c) and (d) are 346 and 376 - so your solution of 346 for both has got me perplexed.

I know what happens when the source and object move - I know what the wavefronts look like. I just don't understand WHY if the apparent speed of sound moves when the object moves WHY the apparent speed of sound DOESN'T move when the source moves. WHY should it change one way and not the other way.

 

[Dick]

The problem is poorly stated. It should explicitly say that the speed they are asking for is relative to the observer. That's what they mean by apparent. No motion of the sound source can make it travel faster through air. Motion of the observer can make it seem faster or slower to him because he can catch up with or lag behind the sounds motion in the air. The situation in relativity with light is completely different.

 

[hikaru1221]

Nope. None of those solutions really help.

The solution states that the apparent speed of sound changes when the object moves.

Hikaru - if you note the answers for (c) and (d) are 346 and 376 - so your solution of 346 for both has got me perplexed.

No, 346m/s is the speed of sound wave in the medium, regardless of the speed of the source. In (c), the observer is stationary, so the relative speed is 346. In (d), the observer moves away from the wave front at 30m/s, so the relative speed is 376. I think the word "apparent" means "observed" or "relative to the observer" or "apparent to the observer".

I know what happens when the source and object move - I know what the wavefronts look like. I just don't understand WHY if the apparent speed of sound moves when the object moves WHY the apparent speed of sound DOESN'T move when the source moves. WHY should it change one way and not the other way.

I don't get what you're perplexed about.

 

[hydrogen1]

Hey Nikstar,

Filip Larsen and Borek are both right but maybe I can describe it to you this way.

The velocity is dictated by the medium so if you move into the velocity of the waves V apparent increases. If you move away from the waves then Vapp decreases relative to your frame.

For example
c) Fire truck is moving toward you at 20m/s well who cares because the waves are still moving toward you at 346m/s. See what I mean. YES the frequency of the waves increases and the doppler effect is noticed. Remember do not bring doppler effect into this problem

d) In this problem the waves are still moving 346m/s because of the medium but I am going 30m/s directly into them from the back of the source. Vapp is 376m/s

The authors solution is correct and I believe the wording is fine just remember to not consider doppler effect at all. Try and see how the doppler effect still takes place in the context of what I have written.

 

[nikstar]

Thanks Hydrogen1 and Dick. It makes a little more sense - so you are just looking at the speed apparent to the observer, so in part (d) even though the truck is traveling at 20m/s and you are traveling at 30m/s you only take into account your 30m/s?

What a very strange question...

 

[hydrogen1]

The conditions of the medium(air) put a limit on the speed of sound at 346m/s.
Whether the source is moving or not the sound will travel at 346m/s to a stationary observer.

 

[ricegrad]

Note that the hint you provided as well - "If you are moving towards a source of sound, the speed of sound will be the sum of the speed of sound and your own speed" - does not say to take into account the speed of the emitter. Take into account only the speed of sound (a value that is known), and the speed of the observer.

As I understand it, the vehicle's motion only gives you the "points of origin" for the sound waves. For each individual wave of sound, the source is not the moving vehicle, it is the point at which the vehicle produced the wave. The "source" is considered to be not moving, in the case of sound speeds and relative sound speeds.

(my own perspective as a student, after reading this topic)