A copper rod 50 cm long is fixed in the middle.

A copper rod 50 cm long is fixed in the middle. It is necessary to find the number of longitudinal natural vibrations of the rod in the range from 20 to 50 kHz and their corresponding frequencies. This task has number 40698.

To solve the problem, we use the formula for calculating the frequency of longitudinal natural vibrations of the rod:

f = (n * c) / (2L),

where f is the oscillation frequency, n is the harmonic number, c is the speed of propagation of longitudinal waves in the material of the rod, L is the length of the rod.

The speed of propagation of longitudinal waves in copper is approximately 5000 m/s. Substituting the data into the formula, we get:

f20 = (20 * 5000) / (2 * 0.5) ≈ 100000 Hz

f50 = (50 * 5000) / (2 * 0.5) ≈ 250000 Gc

Thus, the number of longitudinal natural vibrations of the rod in the range from 20 to 50 kHz is 31, and their corresponding frequencies are in the range from 100 to 250 kHz.

A copper rod 50 cm long is fixed in the middle

We present to your attention a unique digital product - “A copper rod 50 cm long is fixed in the middle.” This product will allow you to expand your knowledge in the field of physics and mechanics.

With this product you can calculate the number of longitudinal natural vibrations of a copper rod 50 cm long in the range from 20 to 50 kHz and determine their corresponding frequencies. To solve the problem, you need to use the formula to calculate the frequency of the longitudinal natural vibrations of the rod.

The product is presented in electronic format, which will allow you to quickly and conveniently obtain the necessary knowledge. By purchasing this product, you receive a detailed solution to the problem with a record of the formulas and laws used in the solution, the derivation of the calculation formula and the answer.

Don't miss the opportunity to purchase this unique digital product and expand your horizons in the field of physics and mechanics!

We present to your attention a unique digital product - “A copper rod 50 cm long is fixed in the middle.” This product will help you calculate the number of longitudinal natural vibrations of a 50 cm long copper rod in the range from 20 to 50 kHz and determine their corresponding frequencies.

To solve the problem, it is necessary to use the formula for calculating the frequency of longitudinal natural vibrations of the rod: f = (n * c) / (2L), where f is the vibration frequency, n is the harmonic number, c is the speed of propagation of longitudinal waves in the material of the rod, L is the length rod. The speed of propagation of longitudinal waves in copper is approximately 5000 m/s.

Substituting the data into the formula, we get:

f20 = (20 * 5000) / (2 * 0.5) ≈ 100000 Hz f50 = (50 * 5000) / (2 * 0.5) ≈ 250000 Hz

Thus, the number of longitudinal natural vibrations of the rod in the range from 20 to 50 kHz is 31, and their corresponding frequencies are in the range from 100 to 250 kHz.

The product is presented in electronic format, which will allow you to quickly and conveniently obtain the necessary knowledge. By purchasing this product, you receive a detailed solution to the problem with a record of the formulas and laws used in the solution, the derivation of the calculation formula and the answer. Don't miss the opportunity to purchase this unique digital product and expand your horizons in the field of physics and mechanics! If you have any questions about solving the problem, please contact me - I will try to help.

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This product is a copper rod 50 cm long, which is fixed in the middle. For a given rod, it is necessary to find the number of longitudinal natural vibrations in the range from 20 to 50 kHz and the corresponding frequencies.

To solve the problem, it is necessary to use a formula to calculate the natural vibration frequency of the rod depending on its length and material:

f_n = n*v/2L,

where f_n is the frequency of the nth natural vibration, v is the speed of propagation of longitudinal waves in the rod material, L is the length of the rod, n is the number of natural vibrations.

For a copper rod, the speed of propagation of longitudinal waves can be taken equal to 3810 m/s.

Thus, for a given rod, the following longitudinal natural vibrations are possible in the specified frequency range:

• 20 kGc: n=2, f_n=19,050 Gc
• 30 kGc: n=3, f_n=28,575 Gc
• 40 kGc: n=4, f_n=38,100 Gc
• 50 kGc: n=5, f_n=47,625 Gc

Answer: The number of longitudinal natural vibrations in the range from 20 to 50 kHz is 4, the corresponding vibration frequencies are 19.050 Hz, 28.575 Hz, 38.100 Hz and 47.625 Hz.

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