Frequency and wavelength of vertical string wave

What effect does this have on the velocity of the wave?In summary, the velocity of the wave remains constant as it travels up the rope, while the tension of the particles on the string increases. This increase in tension causes the wavelength of the wave to increase as well.
  • #1
ming

Homework Statement


A long, heavy rope hangs straight down from a high balcony on an apartment building. The lower end of the rope hangs about 1.0 m above the ground. If you grab onto the lower end and waggle it back and forth with constant frequency f, a wave travels up the rope. What would happen to the frequency and wavelength of the wave as it travels up the rope? For each property, state whether it would increase, decrease or remain the same, and explain briefly.

Homework Equations


v=fλ

The Attempt at a Solution


Due to gravity the velocity of the wave should be constantly decreasing as it travels upwards. However, I am not sure whether f decreases, λ decreases or something I have never thought of.
 
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  • #2
Welcome to PF!
ming said:
Due to gravity the velocity of the wave should be constantly decreasing as it travels upwards.
A ball projected vertically upward will slow down due to gravity. But a wave traveling up the rope might not act like the ball. So, you need to reconsider this.

What properties of the rope determine the speed of a wave on the rope?
 
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  • #3
TSny said:
Welcome to PF!
A ball projected vertically upward will slow down due to gravity. But a wave traveling up the rope might not act like the ball. So, you need to reconsider this.

What properties of the rope determine the speed of a wave on the rope?
So the velocity of the wave stays constant. It also seems the tension of the particles on the string increases as you go up as well. I'm guessing wavelength would increase because of this?
 
  • #4
ming said:
So the velocity of the wave stays constant.
Why do you say the velocity will remain constant? Did you try to answer the question I posed in post #2?

It also seems the tension of the particles on the string increases as you go up as well.
Yes, the tension increases as you move up the string.
 

Related to Frequency and wavelength of vertical string wave

What is the relationship between frequency and wavelength of a vertical string wave?

The frequency and wavelength of a vertical string wave are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation: c = fλ, where c is the speed of the wave, f is the frequency, and λ is the wavelength.

How do I calculate the frequency of a vertical string wave?

The frequency of a wave can be calculated by dividing the speed of the wave by the wavelength. This is represented by the equation: f = c/λ. The speed of a wave can be determined by the properties of the medium it is traveling through, while the wavelength is the distance between two consecutive peaks or troughs of the wave.

What factors can affect the frequency of a vertical string wave?

The frequency of a wave can be affected by the tension and length of the string, as well as the properties of the medium it is traveling through. The tension and length of the string will determine the speed of the wave, while the properties of the medium, such as density and elasticity, can also impact the speed and therefore the frequency of the wave.

How is the wavelength of a vertical string wave measured?

The wavelength of a wave can be measured by measuring the distance between two consecutive peaks or troughs of the wave. This can be done using a ruler or by using specialized equipment such as an oscilloscope. The wavelength is typically measured in units of distance, such as meters or centimeters.

What is the significance of the frequency and wavelength of a vertical string wave?

The frequency and wavelength of a vertical string wave determine its properties, such as its energy and speed. Understanding these properties can help us better understand the behavior and characteristics of waves, which can have practical applications in fields such as acoustics, optics, and telecommunications.

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