Find the distance this spot travels in one period.

  • Thread starter Thread starter justneedhelp81
  • Start date Start date
  • Tags Tags
    Period
Click For Summary
SUMMARY

The discussion centers on calculating the distance a marked spot on a rope travels during one period of a transverse wave. The hand oscillates every 2.5 seconds, with a wave speed of 0.8 m/s and a frequency of 0.4 Hz. The amplitude of the wave is 0.1 m, leading to a total distance traveled by the spot of 0.4 m in one complete oscillation. The key takeaway is that the distance traveled is the total vertical movement, which is four times the amplitude over one period.

PREREQUISITES
  • Understanding of transverse waves and their properties
  • Familiarity with wave equations, specifically y(t) = A sin(2πft)
  • Knowledge of oscillation concepts, including frequency and period
  • Basic trigonometry for calculating distances in wave motion
NEXT STEPS
  • Study the relationship between wave speed, frequency, and wavelength
  • Learn about the concepts of amplitude and its impact on wave motion
  • Explore the derivation and application of wave equations in different contexts
  • Investigate the effects of damping and tension on wave propagation in ropes
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators seeking to clarify concepts related to transverse waves and oscillations.

justneedhelp81
Messages
3
Reaction score
0
Ive been trying this problem for awhile now and I seem to not get it.

A hand holding a rope moves up and down to create a transverse wave on the rope. The hand completes an oscillation in 2.5s, and the wave travels along the string at 0.8 m/s. The amplitude of the wave is 0.1m. The frequency at which the crests pass a given point in space is 0.4 Hz. The distance between the two adjacent crests on the wave is 2m.

a) There is a blue spot drawn onto the rope with a magic marker. Find the distance this spot travels in one period.

I have tried using the equation y(t)=Asin(2*pi*f*t)
which is 0.1m*sin(2*pi*.4*2.5) = .0109 m and I got this wrong. I am not sure where I did go wrong and was wondering if anyone can help me. Thanks.
 
Physics news on Phys.org
justneedhelp81 said:
Ive been trying this problem for awhile now and I seem to not get it.

A hand holding a rope moves up and down to create a transverse wave on the rope. The hand completes an oscillation in 2.5s, and the wave travels along the string at 0.8 m/s. The amplitude of the wave is 0.1m. The frequency at which the crests pass a given point in space is 0.4 Hz. The distance between the two adjacent crests on the wave is 2m.

a) There is a blue spot drawn onto the rope with a magic marker. Find the distance this spot travels in one period.

I have tried using the equation y(t)=Asin(2*pi*f*t)
which is 0.1m*sin(2*pi*.4*2.5) = .0109 m and I got this wrong. I am not sure where I did go wrong and was wondering if anyone can help me. Thanks.

This equation gives the vertical position and since the point is moving up and down, calculating the position will not give the distance travelled. (I could move 20 meters to the right and then come back and my position will not have changed but the distance traveled will be 40 meters).

You should just visualize it. Let's say that the point is initially at the very top. Then as the wave passes it will move down for a while and eventually start moving up again. In terms of the amplitude A, what distance does it travel in one period?

Pat
 
crust to crust would be 2m, the one that i calculated, (velocity/frequency)
and in one period does it travel half the distance of amplitude?
 
.1m x 4 = .4m, i think i get it now
 

Similar threads

Distance traveled by a particle in a transverse wave
  • · Replies 2 ·
Replies
2
Views
3K
Spring set makes up a traveling wave
  • · Replies 16 ·
Replies
16
Views
3K
What is the distance traveled by a blue spot on a transverse wave in one period?
  • · Replies 15 ·
Replies
15
Views
4K
Wave equation, wavelenght not given
  • · Replies 6 ·
Replies
6
Views
2K
Number of waves from an oscillating source in one period
  • · Replies 70 ·
3
Replies
70
Views
6K
Answer Checking: Unit 1 Waves Chapter 1
  • · Replies 1 ·
Replies
1
Views
2K
The nature of waves and Periodic waves
  • · Replies 2 ·
Replies
2
Views
4K
Distance from one period to the next, ##e## in helical path.
  • · Replies 1 ·
Replies
1
Views
1K
Expression y(x,t) for sinusoidal wave traveling along a rope
  • · Replies 6 ·
Replies
6
Views
4K
Calculate Speed, Freq & Wavelength of Transverse Waves
  • · Replies 8 ·
Replies
8
Views
30K