Finding the Longest Wavelength of Standing Waves on a 254.0 cm String

In summary, the question is asking for the longest wavelength for standing waves on a 254.0 cm long string with fixed ends, and the answer can be found using the equations k(n) = n*pi/L and wavelength(n) = n*pi/k(n). The conversation also discusses how a wave can be made on a string with fixed ends.
  • #1
kathyt.25
49
0

Homework Statement


What is the longest wavelength for standing waves on a 254.0 cm long string that is fixed at both ends?


Homework Equations





The Attempt at a Solution


When x = L (length of string):

k(n) = n*pi / L
wavelength (n) = n*pi / k(n)

I got the answer, I just don't understand why these equations are used in my textbook to find this particular answer.
 
Last edited:
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  • #2
"how can a wave be made?"

Imagine pulling on the rope hard, to make it taut. You could then make the rope vibrate like a guitar string.

A wave has to be set up in the rope to make it vibrate. Obviously, the fixed ends can't be vibrating, which sets restrictions on the permitted wavelengths. So: what's the longest possible wavelength?
 

Related to Finding the Longest Wavelength of Standing Waves on a 254.0 cm String

1. How is the longest wavelength of standing waves on a 254.0 cm string determined?

The longest wavelength of standing waves on a 254.0 cm string is determined by dividing the length of the string by 2. This is because the longest wavelength corresponds to the fundamental frequency, which is equal to half of the string's total length.

2. What is the formula for calculating the longest wavelength of standing waves on a string?

The formula for calculating the longest wavelength of standing waves on a string is λ = 2L, where λ is the wavelength and L is the length of the string.

3. Can the longest wavelength of standing waves on a 254.0 cm string be longer than the length of the string?

No, the longest wavelength of standing waves on a 254.0 cm string cannot be longer than the length of the string. This is because the string can only vibrate up and down, creating standing waves with a maximum wavelength equal to its length.

4. How does the tension and mass of the string affect the longest wavelength of standing waves?

The tension and mass of the string have an inverse relationship with the longest wavelength of standing waves. As the tension increases, the wavelength decreases and vice versa. Similarly, as the mass of the string increases, the wavelength decreases and vice versa.

5. Can the longest wavelength of standing waves on a 254.0 cm string be changed?

Yes, the longest wavelength of standing waves on a 254.0 cm string can be changed by altering the length, tension, or mass of the string. This can be done by adjusting the string's position, tightening or loosening it, or adding weights to it.

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