Chapter 8: Sound

[arexia]

Hi,

For Q12 (in the online Q&A section), the answer says:
"Knowing that vY ∼ 1/(√ ρY), we get: New velocity (vX) = 1/√(2ρY) = 1/(√2) x 1/(√ρY) = 1/(√2) x vY Thus (vX)/(vY) = 1/√2"

But in the answer key, the ratio vX:vY is 1:√2.

Should it be 1:1/√2, or am I missing something?

Thanks

[goldstanda3269]

Hi,

For Q12 .... Thus (vX)/(vY) = 1/√2"

But in the answer key, the ratio vX:vY is 1:√2.

Should it be 1:1/√2, or am I missing something?

A fraction is a ratio, thus a fraction is a proportion,

(vX)/(vY) = 1/√2

can be translated thus: (vX) is to (vY) as 1 is to √2.

And so the answer is correct.

If you have the current edition of the GS book, see the GAMSAT Math section on proportions GM 1.6 and/or fractions GM 1.4.

[brad.willo2670]

Hi there,

Question 6: I understand the way in which the problem was solved, but I do not recall coming across learning the relationship between wave length and 'detection'? Which part of the text details this relationship?

Thanks in advance,
Brad

[goldstanda3269]

Question 6: I understand the way in which the problem was solved, but I do not recall coming across learning the relationship between wave length and 'detection'? Which part of the text details this relationship?

Good point. ACER often, but not always, would provide guidance for such a question. We have updated the question and somewhat modified the calculation based on recent trends. Enjoy!

NB: the next free webinar... www.gamsat-prep.com/GAMSAT-free-online-seminar/

[Sandi]

Hi there,

8.5.1 Doppler Effect Problem

In the book, the final answer is 17.9m/s but when I work out the calculation the answer is approximately around 142m/s because it is 86722/608 (according to my calculation). Am I doing something wrong?

Thanks,
Sandi

[jeanne_gsgamsat]

Hi there,

8.5.1 Doppler Effect Problem

In the book, the final answer is 17.9m/s but when I work out the calculation the answer is approximately around 142m/s because it is 86722/608 (according to my calculation). Am I doing something wrong?

Yes, the problem is that you did not follow the proper order of operations. You can't ADD 277 directly to 331. You must first multiply -262 x 331 and then divide that number by 277 and then finally add that total to 331.

To be sure that you follow the proper order of operations, please consider going back to Chapter 1 GAMSAT Maths section 1.2.3.

Step by step:

vs = -262(331)/277 + 331
vs = -86722/277 + 331
vs = -313 + 331
vs = 18 m/s

[Sandi]

That makes sense! Thank you!

[HunterEd]

6) Ultrasound is an important medical imaging tool. The wavelength used in ultrasound sets the limit to the smallest-sized objects that can be detected.

Consider a small kidney stone of 2.0 millimetres in size, approximately what minimal frequency of ultrasonic waves is necessary to detect this object? (Note: ultrasonic waves travel at approximately 1.5 x 103 m/s in the body)
A) 1.3 x 10-5 Hz
B) 130 kHz
C) 7.5 x 10-5 Hz
D) 750 kHz

Explanation: To be detected, according to the information provided, the wavelength of the wave must be of the order of the object’s size. For an object of 2.0 x 10-3 m in size (= 2 mm) to be detected (FYI: a small kidney or gallbladder stone), the wavelength should accordingly be: λ = 2.0 x 10-3 m.

f = v/λ (you don't need the equation; you can just note that Hz is the inverse of seconds and then use dimensional analysis, i.e., follow the units as done below)
f = (1.5 x 103 m/s) / (2 x 10-3 m)
f = (15 x 102 m/s) / (2 x 10-3 m)
f = 7.5 x 10^5 s-1 = 750 x 10^3 s-1
Recall that Hz = s-1, thus:
f = 750 x 103 Hz = 750 kHz

Correct me if i'm wrong but shouldn't this say, 750 x 10^4 s-1 instead of 750 x 10^3 s-1 ?

thank you

[goldstanda3269]

f = 7.5 x 10^5 s-1 = 750 x 10^3 s-1
......

Correct me if i'm wrong but shouldn't this say, 750 x 10^4 s-1 instead of 750 x 10^3 s-1 ?

The number in the explanation is correct:

f = 7.5 x 10^5 s-1 = 750 x 10^3 s-1

Some students would remember it this way: If you add 2 decimal points to the factor (i.e. 7.5 to 750) then you must remove 2 from the power of ten (i.e. 10^5 to 10^3) in order to maintain equality.

[HunterEd]

oh wow, I must have had physics-brain yesterday. Sorry to waste your time!

[goldstanda3269]

As long as you're studying/practicing, no time is wasted! Keep it up!

[SeoM]

Hi, I'm really sorry but I am stuck on the explanation for the answer to question 10.

In the explanation, it says "10 log10 (a) = 20, or after simplification 10^log10(a) =a=10^2=100"

I don't understand the 'simplified' why 10^log10(a) =a . I know this is probably a basic log problem but I dont understand it and am hoping you could please shed some light on it for me please?

[goldstanda3269]

Hi, I'm really sorry but I am stuck on the explanation for the answer to question 10.

In the explanation, it says "10 log10 (a) = 20, or after simplification 10^log10(a) =a=10^2=100"

I don't understand the 'simplified' why 10^log10(a) =a . I know this is probably a basic log problem but I dont understand it and am hoping you could please shed some light on it for me please?

Log rules are not so much about understanding but certainly need to be memorized. This particular rule is number 5 in the book ( GAMSAT Maths in the Gold Standard GAMSAT Book 2, GM 3.7 and 3.8 ) or you can see the rule online here:
https://www.gamsat-prep.com/gamsat-math ... hmicScales

You can also go to 13:47 in the General Chemistry video "New: Buffers" to see this specific log rule in action.

Basically, in order to isolate "a" in question 10, we need to get rid of the log base 10 and the only way to do this is to raise both sides to the power of 10 (this is rule 5 in GM 3.7.1).

[NooraALUBAIDE]

I would like to ask that as we have been informed before ( remember that tiny differences at the very top of log scales are massively more important than huge differences at the lower part of the scale)

so according to this information if I choose the range between 100 and 90 dB (20-30 Hz ) would it be wrong ? knowing that it's at the top of the scale too ? or the choice came in accordance with the given answers choices.

[goldstanda3269]

I would like to ask that as we have been informed before ( remember that tiny differences at the very top of log scales are massively more important than huge differences at the lower part of the scale)

so according to this information if I choose the range between 100 and 90 dB (20-30 Hz ) would it be wrong ? knowing that it's at the top of the scale too ? or the choice came in accordance with the given answers choices.

Which question are you referring to in GAMSAT Physics Chapter 8?