How can I solve light and sound wave problems?

In summary, the conversation is about seeking assistance with various physics problems. The first problem involves a musical instrument consisting of a can with a string stretched across the open end. The second problem involves a convex spherical mirror and a plane mirror, while the third problem involves a concave mirror and a luminous object. The conversation also includes the asker's attempts at solving the problems and a request for further help. The final question is about the effect of increasing the tension in the string of the musical instrument by a factor of four.
  • #1
JM2107
[SOLVED] Light and Sound wave problems PLEASE HELP!

I have a few questions that I need assistance understanding and solving. I would greatly appreciate any help provided to me.

1. A musical instrument is invented that consists of a can with length L and diameter L/6. The top of the can is cut out, and a string is stretched across this open end of the can. The tension in the string is adjusted so that the frequency of the fifth harmonic for the longitudinal sound in the air column in the can equals the frequency of the sixth harmonic for transverse waves on the string.

- What is the mathematical relationship between the speed of the transverse waves on the string and the speed of sound waves in the air?

- What happens to the sound produced by the instrument if the tension in the string is increased by a factor of four? (I would appreciate more in depth comment on this particular question)


2. A convex spherical mirror with a focal length of magnitude 24.0cm is placed 16.0cm to the left of a plane mirror. An object 0.80cm tall is placed midway between the surface of the plane mirror and the vertex of the spherical mirror. The spherical mirror forms multiple images of the object.

- Where are the two images of the object formed by the spherical mirror that are closest to this mirror, and how tall is each of them? Are the images real or virtual, inverted or upright?


3. A luminous object is 5.2m from a wall. You are to use a concave mirror to project an inverted image of the object on the wall, with the image 4.00 times the size of the object.

- How far should the mirror be from the wall, and what should its radius of curvature be and is the image real or virtual?


Once again, I appreciate feedback/responses from anyone that can help me. Just to add; I have tried to solve number 1 in this post and got some figures for the two speeds. I tried to solve the second question but when I realized that the light wave keeps bouncing off the mirrors I was sort of at a loss as to how to completely answer the questions. So mainly I am asking for more focus to be put on the second question for the first problem and the second and third problems as a whole if it isn’t asking for too much. Thanks for the help once again.
 
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  • #2
JM2107,

Before giving assistance, I like to see how you started these problems. I am going to give some very general comments, and get specific only after I see what you have done.

Originally posted by JM2107
1. A musical instrument is invented that consists of a can with length L and diameter L/6. The top of the can is cut out, and a string is stretched across this open end of the can. The tension in the string is adjusted so that the frequency of the fifth harmonic for the longitudinal sound in the air column in the can equals the frequency of the sixth harmonic for transverse waves on the string.

- What is the mathematical relationship between the speed of the transverse waves on the string and the speed of sound waves in the air?

In both cases, the speed v of the wave is related to the frequency f and the wavelength λ by:

v=fλ

You are explcitly given a relation between the two frequencies, and you can look up the speed of sound in air.

- What happens to the sound produced by the instrument if the tension in the string is increased by a factor of four? (I would appreciate more in depth comment on this particular question)

There should be a relation in your book relating wave speed to tension and linear mass density.

2. A convex spherical mirror with a focal length of magnitude 24.0cm is placed 16.0cm to the left of a plane mirror. An object 0.80cm tall is placed midway between the surface of the plane mirror and the vertex of the spherical mirror. The spherical mirror forms multiple images of the object.

- Where are the two images of the object formed by the spherical mirror that are closest to this mirror, and how tall is each of them? Are the images real or virtual, inverted or upright?

3. A luminous object is 5.2m from a wall. You are to use a concave mirror to project an inverted image of the object on the wall, with the image 4.00 times the size of the object.

- How far should the mirror be from the wall, and what should its radius of curvature be and is the image real or virtual?

Try drawing the ray diagrams and setting up the equations. We will help you solve and interpret their solutions properly, but you have to give us something to help you with.

Thanks,
 
  • #3
To get more specific

I have solved all of the problems with the exception of one. The question is

What happens to the sound produced by the created instrument if the tensin in the string is increased by a factor of four?

This is what I think but I am convinced that it is not right: If the force of the tension of the string in the instrument is increased by a factor of four, then the velocity of the wave on the string will ultimatly end up doubling; thereby also meaning that the frequency of the wave would double as well. The wavelength, however, will not increase but remain constant and the amplitude of the wave will deacrease, by some factor, as a direct result of the tension increase in the string. This means that the pitch of the frequency would double.

Could you please tell me whether I am right or not, and if I am wrong, could you help me to understand what really goes on in this senario.
 
Last edited by a moderator:
  • #4
Yes, that is correct. The wave speed v is related to the tension τ and the linear mass density μ by the following relation:

v=(τ/μ)1/2

Since you are not changing the length or the mass, μ does not change. So simply increasing the tension by 4 doubles the velocity. Since the wavelength does not change, the frequency must also double.
 

1. What is the difference between light and sound waves?

Light waves are electromagnetic waves that can travel through a vacuum at the speed of light. They are made up of oscillating electric and magnetic fields. Sound waves, on the other hand, are mechanical waves that require a medium, such as air or water, to travel through. They are made up of compressions and rarefactions of molecules in the medium.

2. How does the wavelength of a wave affect its properties?

A shorter wavelength means a higher frequency and energy for both light and sound waves. This determines the color or pitch of the wave. Additionally, shorter wavelengths can allow waves to diffract or bend around objects more easily.

3. How do light and sound waves interact with each other?

Light and sound waves do not directly interact with each other, as they are different types of waves. However, they can both be reflected, refracted, and diffracted by objects, which can cause them to interact indirectly.

4. What are some common applications of light and sound waves?

Light waves have numerous applications, including communication (such as in fiber optics), medical imaging (such as X-rays and MRI), and for seeing objects. Sound waves are commonly used for communication (such as in telephones and microphones), medical imaging (such as ultrasounds), and for hearing sounds.

5. How do light and sound waves travel through different mediums?

Light waves can travel through a variety of mediums, including air, water, and even some solids. However, the speed of light may vary depending on the medium. Sound waves also travel through different mediums, but they require a medium to travel through. The speed of sound also varies depending on the medium's density and elasticity.

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