# Wave Speed & Wavelength of Harmonic Oscillation on Slinky

• CMATT
In summary: I see where I made a mistake in assuming that the time and length were related. I also realized that the total length of the Slinky is actually double the length of one wavelength since it includes both the compression and rarefaction. Thanks again for pointing that out!
CMATT
(a) A wave traveling on a Slinky® that is stretched to 4.5 m takes 2.6 s to travel the length of the Slinky and back again. What is the speed of the wave?
For this one, I did v = d/t
= 4.5 m / 2.6 s
= 1.73 m/s

Then I did v = (1.73)(2) = 3.46 m/s
This is correct

(b) Using the same Slinky stretched to the same length, a standing wave is created which consists of 5 antinodes and 6 nodes including both ends. What is the wavelength of the wave?
I keep getting stuck on this one, and (c) below. I know this answer should be in meters.

(c) At what frequency must the Slinky be oscillating?
I know this answer should be in Hz.

Im not sure which equations to use for (b) and (c)

Any help is greatly appreciated!

CMATT said:
(a) A wave traveling on a Slinky® that is stretched to 4.5 m takes 2.6 s to travel the length of the Slinky and back again. What is the speed of the wave?
For this one, I did v = d/t
= 4.5 m / 2.6 s
= 1.73 m/s

Then I did v = (1.73)(2) = 3.46 m/s
This is correct
Not really. There's no good reason to divide 4.5 m by 2.6 s as those two quantities don't have anything to do with each other.

(b) Using the same Slinky stretched to the same length, a standing wave is created which consists of 5 antinodes and 6 nodes including both ends. What is the wavelength of the wave?
I keep getting stuck on this one, and (c) below. I know this answer should be in meters.
Start by drawing a picture of a snapshot of the standing wave. You can then identify what fraction of the length of the Slinky is equal to one wavelength.

(c) At what frequency must the Slinky be oscillating?
I know this answer should be in Hz.

Im not sure which equations to use for (b) and (c)

Any help is greatly appreciated!

CMATT
CMATT said:
(a) A wave traveling on a Slinky® that is stretched to 4.5 m takes 2.6 s to travel the length of the Slinky and back again. What is the speed of the wave?

Note particularly the length, total length and travel time

Dave

You need to identify the nodes and anti-nodes.
What is the distance between them?
A diagram would be useful in this regard.
The waves being referred to are probably compressional waves, so if you have studied sound waves which
travel by compressions and rarefactions, then how do these relate to wavelength.
Also, you know that if the Slinky is stretched to the same length then the tension in the Slinky is constant.
How does tension relate to frequency and wavelength?
Hope you find these comments useful.

J Hann said:
You need to identify the nodes and anti-nodes.
What is the distance between them?
A diagram would be useful in this regard.
The waves being referred to are probably compressional waves, so if you have studied sound waves which
travel by compressions and rarefactions, then how do these relate to wavelength.
Also, you know that if the Slinky is stretched to the same length then the tension in the Slinky is constant.
How does tension relate to frequency and wavelength?
Hope you find these comments useful.

Yes I made a diagram, it was very useful.
I figured it out! Thank you for your help

davenn said:
Note particularly the length, total length and travel time

Dave

davenn

## 1. What is a harmonic oscillation on a slinky?

A harmonic oscillation on a slinky is when the slinky is stretched or compressed and is released, causing it to move back and forth in a regular pattern. This is caused by the slinky's ability to store and release potential energy.

## 2. What determines the wave speed of a harmonic oscillation on a slinky?

The wave speed of a harmonic oscillation on a slinky is determined by the tension of the slinky, the mass of the slinky, and the length of the slinky. These factors affect how quickly the energy is transferred through the slinky and therefore determine the wave speed.

## 3. How does wavelength affect a harmonic oscillation on a slinky?

The wavelength of a harmonic oscillation on a slinky is the distance between two consecutive crests or troughs of the wave. The wavelength affects the amplitude of the wave, as well as the frequency and speed of the wave.

## 4. Can the wave speed and wavelength of a harmonic oscillation on a slinky be changed?

Yes, the wave speed and wavelength of a harmonic oscillation on a slinky can be changed by altering the tension, mass, or length of the slinky. Additionally, the type of disturbance applied to the slinky can also affect the wave speed and wavelength.

## 5. What is the relationship between wave speed and wavelength in a harmonic oscillation on a slinky?

The wave speed and wavelength in a harmonic oscillation on a slinky have an inverse relationship. This means that as the wavelength increases, the wave speed decreases, and vice versa. This relationship is described by the equation v = λf, where v is the wave speed, λ is the wavelength, and f is the frequency of the wave.

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