Multiple-Choice Questions on the Behaviour of Waves and Light 😁

[lpettigrew]

Homework Statement

Hello, I have several multiple choice questions below which I have answered and given reasoning to but due to my unfamiliarity with the topic I was wondering whether someone could evaluate my answers to look for errors or suggest possible improvements? Thank you very much for any help I am earnestly grateful

Question 1: Light travels from a medium with a refractive index n1 to a medium with refractive index n2, which of the following is necessary for total internal reflection to occur?
a. n1=n2
b.n1>n2
c.n1<n2
d. n1≤n2

Question 2: Which has a wavelength ranging between 10-14 m and 10-10 m?
a. Visible light
b. γ-rays
c. Ultrasound
d. X-rays

Question 3; I have also attached the diagram to this question.
The diagram exhibits a wave on a rope at an instant in time. At this point in time, X is at its maximum displacement and Y is at its equilibrium position. Which describes the motion of points X and Y as the wave moves to the right?

a. Y rises, X falls
b. X rises, Y falls
c. Y rises; X is at rest
d. X rises; Y rises

Question 4; What is the fundamental frequency of a string in its third overtone when it plays a note of 220 Hz?

a. 880 Hz
b. 1100Hz
c. 55Hz
d. 44Hz

Question 5; I have attached a diagram tat is intended to be used for all aspects of this question.
i. Identify the points in anti-phase

a. (O & B), (D & F), (A & E), (C & G)
b. (O & B), (B & D), (D & F), (A & C), (C & E), (E & G)
c. (O&D),(B&E),(D&E),(C&G),(G&F)
d. (O, B, D & F), (A, E, C & G)

ii. Identify the points in phase

a.(O & D), (A & E), (C & G), (B & F)
b.(O, B, D & F), (A, E, C & G)
c.(O, B, D & F), (A & E), (C & G)
d.(O & B), (D & F), (A & E), (C & G)

iii. Identify the points with a phase difference of π / 2

a.(O & D), (A & E), (C & G), (B & F)
b.(O, A, D & E), (B, C, F & G)
c.(O & B), (B & D), (D & F), (A & C), (C & E), (E & G)
d.(O & A), (A & B), (B & C), (C & D), (D & E), (E & F), (F & G)

iv. Calculate the wave speed

a.50 ms-1
b.0.5 ms-1
c. 0.25 ms-1
d. 8 ms-1

Question 6;The fundamental frequency of a string is 440 Hz and the speed of sound is 340 ms-1.
Find the length of the string is
a. 1.3 m
b. 39cm
c.1.5m
d. 77cm

Relevant Equations

v=f*λ

Question 1; The conditions for total internal reflection are:
-That light is traveling from an optically denser medium (higher refractive index) to an optically less dense medium (lower refractive index)
- That the angle of incidence is greater than the critical angle.
Therefore, I conclude that the correct answer is b, n1>n2

Question 2; I believe that the correct answer is b. γ-rays.

Question 3; I believe that the correct answer is d, X rises and Y rises as the wave oscillates to the right the positions of X and Y will both increase originally as they travel to the wave peak. As the wave continues to travel, the positions of X and Y will respectively fall as they follow the trough of the wave and so on.

Question 4; I believe that the correct answer is c, 55Hz since harmonics are integer multiples of the fundamental frequency. Therefore, if the 4th harmonic is 220Hz the fundamental frequency will be 220/4=55Hz

Question 5;
i.For sinusoidal signals, when the phase difference 180° or rather

radians the phases are opposite the waves are said to be in antiphase. Hence I think that the correct solution is b. (O & B), (B & D), (D & F), (A & C), (C & E), (E & G)

ii. When two points are in-phase they are separated by a complete wavelength, thus I believe the correct answer is a. (O & D), (A & E), (C & G), (B & F)

iii. A phase difference of π / 2 radians would occur at (O & A), (A & B), (B & C), (C & D), (D & E), (E & F), (F & G), choice d.

iv. Wavelength is shown to be 20cm=0.2m
Frequency = 0.4s to produce 1 wave. In 1 second; 1/0.4=2.5 waves produced per second, therefore, there will be a frequency of 2.5 Hz
v=f*λ
v=2.5*0.2
v=0.5 ms^-1 (choice b)

Question 6;
λ=v/f
λ=2L in the fundamental frequency
2L=340/440
2L=0.772727272…
Since wavelength=2L, 0.772/2=0.3886~0.39m =39cm or choice b.

 

[BvU]

due to my unfamiliarity with the topic

Why take a test if you are unfamiliar with the subject ?

What is the purpose of you post ? PF is not for stamp-approving homework, nor does it replace a decent textbook for all the answers.

If there is a specific question for which you don't understand something, we are of course glad to assist !

 

[lpettigrew]

Why take a test if you are unfamiliar with the subject ?

What is the purpose of you post ? PF is not for stamp-approving homework, nor does it replace a decent textbook for all the answers.

If there is a specific question for which you don't understand something, we are of course glad to assist !

@BvU I actually felt very uncertain upon the subject focus of these questions which I have been revising and attempting to better understand, particularly those in relation to defining the points of phase and anti-phase which have been a source of confusion. It was not my intent to ask for approval but merely to see whether the methods I have used to arrive at my solutions are here appropriate and any improvements I can make in the future. There are no affiliated answers which I can check and I do not have anyone who can help or guide me which is why I thought the PF may be able to assist me. I did not mean to offend.

 

[haruspex]

Answers to 1 and 2 are fine.

X rises and Y rises as the wave oscillates to the right

It doesn't "oscillate" to the right, it moves right. Superimpose the same wave moved a bit to the right. Does it now pass below the point marked Y or above it?

Question 4; What is the fundamental frequency of a string in its third overtone when it plays a note of 220 Hz?
The question is a bit garbled so you may have misread it.
It should read "if a string's third overtone is 220Hz, what is its fundamental frequency?"

I'll look at 5 and 6 later.

 

[lpettigrew]

Answers to 1 and 2 are fine.It doesn't "oscillate" to the right, it moves right. Superimpose the same wave moved a bit to the right. Does it now pass below the point marked Y or above it?

Question 4; What is the fundamental frequency of a string in its third overtone when it plays a note of 220 Hz?
The question is a bit garbled so you may have misread it.
It should read "if a string's third overtone is 220Hz, what is its fundamental frequency?"

I'll look at 5 and 6 later.

@haruspex Thank you for your reply and I apologise for not replying sooner I have not been on the PF for a while. Regarding question 3 I think from what you have stated to imagine superposing the same wave to the right the wave will rise at Y but remain at rest at X?

Question 4; Oh, thank you for putting that more clearly. I thought that the harmonics were multiples of the fundamental frequency. So, the third overtone = 4 * fundamental frequency
If the third overtone is 220 Hz, then surely the fundamental frequency = 220/4=55Hz

Sorry I am still getting this wrong?

Were my answers for questions 5 and 6 correct?

 

[haruspex]

from what you have stated to imagine superposing the same wave to the right the wave will rise at Y but remain at rest at X?

Seems to me that Y will fall, but that combination is not listed.

Yes, 55Hz for 4, and I agree with all your answers for 5 and 6.