Question on Natural Frequencies

[bleedblue1234]

Homework Statement

The speed of transverse waves along a stretched spring is 9.05 meters per second. The spring is 4.70 meters long and is held in place at both ends. What are the first three natural frequencies of the spring? Hint: Draw pictures of what the spring will look like when it is vibrating at the first three harmonics.

The Attempt at a Solution

I just cannot seem to be able to find out the frequency...

 

[bleedblue1234]

never mind I am ok

 

[kerimek]

I would suggest approaching this problem by first understanding the concept of natural frequencies. Natural frequencies are the frequencies at which an object naturally vibrates when disturbed. In the case of a stretched spring, the natural frequencies are determined by its length, tension, and mass.

To find the first three natural frequencies of the spring, we can use the formula f = (1/2L)√(T/m), where L is the length of the spring, T is the tension, and m is the mass per unit length. Plugging in the given values, we get:

f1 = (1/2 * 4.70m)√(T/m) = 0.106 * √(T/m)
f2 = (1/2 * 4.70m)√(2T/m) = 0.149 * √(T/m)
f3 = (1/2 * 4.70m)√(3T/m) = 0.183 * √(T/m)

These are the first three natural frequencies of the spring. To visualize them, you can imagine the spring vibrating at each frequency, with the first harmonic having one full wavelength, the second harmonic having two wavelengths, and the third harmonic having three wavelengths.

I would also suggest drawing diagrams to better understand the concept and to help with the calculations. It is important to note that the natural frequencies of a spring are independent of the amplitude of the vibration, so the frequency remains the same regardless of how far the spring is stretched.

In conclusion, by understanding the concept of natural frequencies and using the given formula, we can easily find the first three natural frequencies of the stretched spring. I hope this helps in solving the problem.