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

In summary: I see.The correct answer is c. The fundamental frequency of a string in its third overtone when it plays a note of 220 Hz is 220/3=55 Hz.
  • #1
lpettigrew
115
10
Poster has been reminded to not post so many questions all in one schoolwork thread
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
\pi
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.
 

Attachments

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  • #2
lpettigrew said:
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 !
 
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  • #3
BvU said:
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.
 
  • #4
Answers to 1 and 2 are fine.

lpettigrew said:
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.
 
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  • #5
haruspex said:
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?
 
  • #6
lpettigrew said:
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.
 

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

1. What is the difference between transverse and longitudinal waves?

Transverse waves are waves in which the particles of the medium vibrate perpendicular to the direction of wave propagation, while longitudinal waves are waves in which the particles of the medium vibrate parallel to the direction of wave propagation.

2. How does the amplitude of a wave affect its energy?

The amplitude of a wave is directly proportional to its energy. This means that the higher the amplitude, the more energy the wave carries.

3. What is the relationship between frequency and wavelength?

The frequency of a wave is inversely proportional to its wavelength. This means that as the frequency increases, the wavelength decreases, and vice versa.

4. How does light travel through different mediums?

Light can travel through different mediums, such as air, water, and glass, because it is an electromagnetic wave. These waves do not require a medium to travel and can move through empty space.

5. What is the difference between reflection and refraction of light?

Reflection is the bouncing back of light when it hits a surface, while refraction is the bending of light as it passes through different mediums at an angle. Reflection follows the law of reflection, while refraction follows the law of refraction.

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