# How Close is a Copper Bar to Breaking Under High Tensile Stress and Sound Waves?

• lizzyb
In summary, the tensile stress in a thick copper bar is 99.5% of its elastic breaking point of 13.0 X 10^10 N/m^2, and a 500 Hz sound wave is transmitted through the material. For part (b), the maximum speed of the particle can be calculated using the equation v_{max} = \omega A, once the maximum displacement (or amplitude) is known. For part (a), the frequency is not related and the equation \Delta P_{max} = \rho v \omega s_{max} can be used, where rho and omega are known. The bulk modulus (B) can be determined using the equation v = \sqrt{\
lizzyb
The tensile stress in a thick copper bar is 99.5% of its elastic breaking point of 13.0 X 10^10 N/m^2. A 500 Hz sound wave is transmitted through the material. (a) What displacement amplitude will cause the bar to break? (b) What is the maximum speed of the particle at this moment?

(b) is easy because one we know the maximum displacement (or amplitude), we may use $$v_{max} = \omega A$$

For (a), though, it seems like the frequency isn't related to this part of the question. If the copper is stretched so far, beyond it's elastic breaking point, then it will break, but how do I determine this? Thank you.

Well, we know that $$\Delta P = 13.0 \times 10^{10} - .995 \times 13.0 \times 10^{10} = 6.5 \times 10^8$$
and we can assume that this is $$\Delta P_{max}$$ and we may use the equation $$\Delta P_{max} = \rho v \omega s_{max}$$ where rho and omega are easily determined.

What about v? The book says $$v = \sqrt{\frac{B}{\rho}}$$ so how would I determine B?

B is the bulk's modulus

## 1. What is a Periodic Sound Wave Q?

A Periodic Sound Wave Q is a type of sound wave that has a repeating pattern or cycle. This means that the sound wave will have a consistent frequency and wavelength.

## 2. How is Periodic Sound Wave Q different from other sound waves?

Periodic Sound Wave Q is different from other sound waves because it has a distinct, repeating pattern. Other sound waves may have varying frequencies and wavelengths, making them non-periodic.

## 3. What is the significance of Periodic Sound Wave Q?

Periodic Sound Wave Q is significant because it is the basis for studying and understanding other types of sound waves. By understanding the properties and behavior of Periodic Sound Wave Q, scientists can apply that knowledge to other sound waves.

## 4. How can Periodic Sound Wave Q be measured and analyzed?

Periodic Sound Wave Q can be measured and analyzed using a variety of tools and techniques such as a microphone, oscilloscope, and frequency analyzer. These tools can measure the amplitude, frequency, and wavelength of the sound wave.

## 5. What are some real-world applications of Periodic Sound Wave Q?

Some real-world applications of Periodic Sound Wave Q include music production, speech recognition technology, sonar and ultrasound imaging, and noise cancellation. It is also used in various industries such as telecommunications, engineering, and medicine.

• Introductory Physics Homework Help
Replies
4
Views
9K
• Introductory Physics Homework Help
Replies
10
Views
5K
• Introductory Physics Homework Help
Replies
1
Views
3K
• Introductory Physics Homework Help
Replies
1
Views
4K
• Introductory Physics Homework Help
Replies
20
Views
11K
• Introductory Physics Homework Help
Replies
5
Views
5K
• Mechanics
Replies
1
Views
1K
• Other Physics Topics
Replies
0
Views
4K
• Introductory Physics Homework Help
Replies
9
Views
6K
• Optics
Replies
12
Views
9K