Solving String Tension: Wavelength, Speed and Frequency

In summary, the conversation discusses the tension and mass of a string, and how these values relate to the speed and frequency of a wave traveling through the string. The first equation, v = sqrt(Tension/(m/L)), is used to calculate the speed of the wave when the wavelength is 1m, resulting in a speed of 283m/s. The second equation, v = f * wavelength, is used to calculate the speed when the wavelength is 0.5m, resulting in a speed of 200m/s. Finally, the frequency is calculated using the equation f = v/wavelength, resulting in a frequency of 400Hz. It is noted that the linear mass density, mu, is constant and does not affect
  • #1
gillyr2
45
0

Homework Statement


string is under tension 400N. A 1m string has mass 5grams. what is the speed if the wavelength is 1m. What is the speed if the wavelength is .5m. What is the frequency?


Homework Equations


v = sqrt(Tension/(m/L))
v = f * wavelength


The Attempt at a Solution



a) v = sqrt(400N / (.005kg/1m) = 283m/s

b) I am confused. whether to use the first or second equation?
v=sqrt(400N/.005kg/.5m) = 200m/s

c) f = v/wl = 200m/.5ms = 400Hz

is this correct?
 
Last edited:
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  • #2
just a push in the right direction would be highly appreciated
 
  • #3
L is the entire length of the string. Why would the linear mass density, something that is inherent and doesn't change with the same string, be changing?
 
  • #4
so for b) would it be 1m for both, or is the speed impossible to derive from that formula?
 
  • #5
If [tex] V=\sqrt{\frac{T}{\mu}}[/tex]

What do you hypothesise if mu and T are always constant?
 

What is string tension?

String tension refers to the amount of force exerted on a string, typically by a musical instrument or other device. It is measured in units of newtons (N) or pounds (lbs).

How does wavelength affect string tension?

The wavelength of a string refers to the distance between two consecutive peaks or troughs in the wave pattern of the string. As the wavelength increases, the string tension decreases, and vice versa.

Does string material affect string tension?

Yes, the material of the string can significantly affect the string tension. Different materials have different densities and elastic properties, which can impact the amount of tension required to produce a certain wavelength, speed, or frequency.

What is the relationship between string speed and tension?

The speed of a string, or the rate at which it vibrates, is directly proportional to the tension on the string. This means that as the tension increases, the speed of the string also increases.

How does frequency relate to string tension?

The frequency of a string, or the number of vibrations it produces per second, is also directly proportional to the string tension. As the tension increases, the frequency also increases, and vice versa.

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