Velocity of Wave in Twice the Radius String: V = root(Tension/mu) * root2

In summary, when the radius of a string is doubled while keeping the tension and material constant, the velocity of a wave traveling along the string is multiplied by root 2. Additionally, doubling the cross-section of the string results in a doubling of the total mass of the string. This does not directly affect the formula for velocity, but it is important to consider when manipulating the equations.
  • #1
lostie100
14
0
A wave travels along a string at a speed of 280m/s. What will the speed if the string is replaced by one made of the same material and under the same tension but having twice the radius?

V = root (Tension/mu)

mu = mass/length

length is 2radii

I manipulated the formulas, however, apparently you divide the velocity by 2, but I found it to be multiplied by root2.
Please show me the manipulation of the formulas...
 
Physics news on Phys.org
  • #2
Assuming uniform density what happens when you double the cross-section of the string that remains the same length? Does the total mass of the string change? By how much?

Plug in your numbers then and see what happens.
 
  • #3
The mass also doubles...but I don't see how it relates to the other formula for velocity...
 

Related to Velocity of Wave in Twice the Radius String: V = root(Tension/mu) * root2

1. What is the formula for calculating the velocity of a wave in a string?

The formula for calculating the velocity of a wave in a string is V = root(Tension/mu) * root2, where V represents velocity, Tension represents the tension in the string, and mu represents the linear mass density of the string.

2. How does the radius of the string affect the velocity of the wave?

The radius of the string does not directly affect the velocity of the wave. However, it does indirectly affect it through the tension and linear mass density of the string, both of which are included in the formula for velocity.

3. What is the relationship between tension and velocity in a wave?

There is a direct relationship between tension and velocity in a wave. As tension increases, the velocity of the wave also increases. This can be seen in the formula, where velocity is directly proportional to tension.

4. How does the linear mass density of the string impact the velocity of the wave?

The linear mass density of the string has an inverse relationship with the velocity of the wave. As the linear mass density increases, the velocity of the wave decreases. This can also be seen in the formula, where velocity is inversely proportional to the square root of the linear mass density.

5. Can this formula be used for any type of string, regardless of material?

Yes, this formula can be used for any type of string as long as the tension and linear mass density are known. However, it is important to note that the linear mass density may vary depending on the material of the string.

Similar threads

Time it Takes for a Transverse Pulse to Travel a Distance "L" Up a Cable Against Gravity?
    • Introductory Physics Homework Help
Replies
13
Views
352
Question about Waves on a String
    • Introductory Physics Homework Help
Replies
2
Views
1K
Propagation of transverse pulse on a string
    • Introductory Physics Homework Help
Replies
6
Views
1K
What is the speed of the string? (wave problem)
    • Introductory Physics Homework Help
Replies
2
Views
7K
Wave speed for non-uniform density?
    • Introductory Physics Homework Help
Replies
6
Views
3K
Wave speed on a string of non-uniform linear mass density
    • Introductory Physics Homework Help
Replies
1
Views
3K
Calculating Mass of a Vibrating String Using Known Quantities
    • Introductory Physics Homework Help
Replies
10
Views
2K
Calculating the length of a string from a standing wave
    • Introductory Physics Homework Help
Replies
4
Views
2K
Calculating Wave Speeds of Steel Guitar Strings
    • Introductory Physics Homework Help
Replies
2
Views
2K
Longitudinal and Transverse waves transmitting at same Veloc
    • Introductory Physics Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top