Find wavelength, frequency and speed of a wave,

In summary,The wavelength of a wave on a rope is determined by the length of the red piece of the line, including one crest and one trough of the wave.
  • #1
selma
3
0
Member warned about posting without the homework template
upload_2016-1-1_23-37-35.png


So I was given this diagram to a wave of a rope.
the following questions i have to answer...

1) Find the wavelength in metres.
2) If the time that the wave takes to move from point X to point Y is 6.0 s, determine the speed of the wave and its frequency
3)Find the speed and wavelength if the frequency of the source changed to 2.0 Hz and explain your reasoning.

I have answered these three mostly but I am doubtful about how correct they are, especially #1 and #3

· Find the wavelength in metres ***(this question I feel was confusing because I wasnt sure if the wavelength is actually 1.6 m or 3.2m)

4.8m / 3 waves = 1.6m per wave

Wavelength is 2/3 of the total distance of rope.

2/3 = 0.67

4.8m x 0.67

Λ= 3.2m

The wavelength is 3.2 m.

· If the time that the wave takes to move from point X to point Y is 6.0 s, determine the speed of the wave and its frequencyΔd= 4.8m

Δt= 6.0 s

Λ= 3.2m

v= Δd/Δt

v= 4.8m/6.0s

v= 0.8m/s

The speed of a wave in this equation is 0.8 metres per second.



f= v/Λ

f= 0.8 m per second/3.2m

f= 0.25 Hz

The frequency of the wave in this equation is 0.25 Hz.3) · Find the speed and wavelength if the frequency of the source changed to 2.0 Hz and explain your reasoning. *****(I came up with several answers but was not really convinced any of them were right)
 
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  • #2
selma said:
View attachment 93899

So I was given this diagram to a wave of a rope.
the following questions i have to answer...

1) Find the wavelength in metres.
2) If the time that the wave takes to move from point X to point Y is 6.0 s, determine the speed of the wave and its frequency
3)Find the speed and wavelength if the frequency of the source changed to 2.0 Hz and explain your reasoning.

I have answered these three mostly but I am doubtful about how correct they are, especially #1 and #3

· Find the wavelength in metres ***(this question I feel was confusing because I wasnt sure if the wavelength is actually 1.6 m or 3.2m)

4.8m / 3 waves = 1.6m per wave
Correct, there is three full wavelength along the rope, why do you think it is not true?
selma said:
Wavelength is 2/3 of the total distance of rope.

2/3 = 0.67

4.8m x 0.67

Λ= 3.2m

The wavelength is 3.2 m.

selma said:
· If the time that the wave takes to move from point X to point Y is 6.0 s, determine the speed of the wave and its frequencyΔd= 4.8m

Δt= 6.0 s

Λ= 3.2m

v= Δd/Δt

v= 4.8m/6.0s

v= 0.8m/s

The speed of a wave in this equation is 0.8 metres per second.
Correct.
 
  • #3
Hi Ehild, thanks so much for your response, I read somewhere that generally the wavelength is 2/3 if the entire wave :S
 
  • #4
selma said:
Hi Ehild, thanks so much for your response, I read somewhere that generally the wavelength is 2/3 if the entire wave :S
I do not understand. The wave is kind of motion, it has no length. The wavelength is the repeating part of the wave in space. In the figure, it is the length of the red piece of line, including one crest and one trough of the wave.
upload_2016-1-2_7-9-28.png
 
  • #5
ehild said:
I do not understand. The wave is kind of motion, it has no length. The wavelength is the repeating part of the wave in space. In the figure, it is the length of the red piece of line, including one crest and one trough of the wave.
View attachment 93907
I am not sure but I did find that somewhere on that web, that generally wavelength is 2/3 of a wave in measurement
 
  • #6
selma said:
I am not sure but I did find that somewhere on that web, that generally wavelength is 2/3 of a wave in measurement
What do you mean on "wave in measurement"? What kind of measurement?
A wave is a motion, it has no length. Have you seen water waves, coming in from the depth of a sea or from a lake towards the shore? Sound is also wave motion. You can hear the sound of thunderstorm from very far away, and you know that the wavelength of the sound is in the range of meters. Do you state that you can hear a bolt only if it is a few meter distance from you ?
You are confused with the standing waves appearing on a rope of finite length. If both ends of the rope are fixed, standing waves appear if the length of the rope L is integer multiple of the half wavelength, that is L=m(λ/2). In that case you get a pattern like in the figure below, but the figure in your first post showed a traveling wave.

https://qph.is.quoracdn.net/main-qimg-b7d7c2be0c89df2bdece35e64227b7b7?convert_to_webp=true
 
Last edited by a moderator:

Related to Find wavelength, frequency and speed of a wave,

1. What is the formula for finding the wavelength of a wave?

The formula for finding the wavelength of a wave is λ = v/f, where λ is the wavelength, v is the speed of the wave, and f is the frequency.

2. How do you calculate the frequency of a wave?

The frequency of a wave can be calculated by dividing the speed of the wave by its wavelength, or by using the formula f = v/λ.

3. What units are used to measure wavelength?

Wavelength is typically measured in meters (m), but it can also be measured in other units such as nanometers (nm) or centimeters (cm).

4. How does the speed of a wave relate to its frequency and wavelength?

The speed of a wave is directly proportional to its frequency and inversely proportional to its wavelength. This means that as the frequency increases, the speed of the wave also increases, while a longer wavelength will result in a slower speed.

5. Can the speed of a wave change?

Yes, the speed of a wave can change depending on the medium it is traveling through. The speed of a wave is typically slower in denser mediums, such as water or solids, while it is faster in less dense mediums, such as air or gases.

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