Displacement of a Transverse Wave on a String Question

In summary, the conversation was about determining the period, wavelength, and phase velocity of a transverse wave on a string, as well as calculating the average kinetic energy per metre of the wave. The calculations for both parts were confirmed to be correct. The equation for kinetic energy in this case is Ek = 1/2 * (mass per unit length) * (angular frequency)^2 * (amplitude)^2 * wavelength, and fractions can be written using the "frac" tag in the "Above and Below" section.
  • #1
craig.16
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0

Homework Statement


Question 1
(a) The displacement of a transverse wave on a string is described by:
y(x, t) = 0.01 sin(4x + 200t + [tex]\pi[/tex]), where all quantities are expressed in SI units.
i) Determine values (with appropriate units) for the period, wavelength, and phase
velocity of the wave. [3]
ii) Determine from first principles the average kinetic energy per metre of this wave on a
string of mass per unit length 5 × 10 -2 kg m-1.


Homework Equations


y(x,t)=Asin(kx+[tex]\omega[/tex]t)
Ek=1/2[/tex]mv2

The Attempt at a Solution


For part (i):
period, t=2[tex]\pi[/tex]/[tex]\omega[/tex]=2[tex]\pi[/tex]/200=[tex]\pi[/tex]/100=0.0314 seconds (3dp)
wavelength, [tex]\lambda[/tex]=2[tex]\pi[/tex]/k=2[tex]\pi[/tex]/4=[tex]\pi[/tex]/2= 1.57 m (3 sf)
phase velocity, v=[tex]\omega[/tex]/k=200/4=50ms-1

For part (ii):

Ek=1/2[/tex]mv2=1/2[/tex](5*10-2)(1.57)(50)2=98.1J

Just need confirmation on whether the first part is correct. As for the second part it was a blatant guess by using the SI units and knowing the original equation for kinetic energy, so I need some help on this one if it is incorrect. Also how do you do a fraction on this properly? I tried the first one in the "Above and Below" section but that isn't right. Thanks in advance.
 
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  • #2




Hello! Your calculations for the first part seem to be correct. As for the second part, you are on the right track. The equation for kinetic energy in this case would be Ek = 1/2 * (mass per unit length) * (angular frequency)^2 * (amplitude)^2 * wavelength. So, plugging in the values from the given equation, we get:

Ek = 1/2 * (5 * 10^-2) * (200)^2 * (0.01)^2 * 1.57 = 98.1 J

So, your answer is correct! As for fractions, you can use the "frac" tag in the "Above and Below" section. For example, if you want to write 1/2, you can type [tex]\frac{1}{2}[/tex]. I hope this helps. Keep up the good work!
 

1. What is a transverse wave on a string?

A transverse wave on a string is a type of wave where the particles of the medium (the string) oscillate perpendicular to the direction of the wave's propagation. This means that the wave travels horizontally while the particles on the string move up and down.

2. What causes displacement in a transverse wave on a string?

Displacement in a transverse wave on a string is caused by the energy of the wave being transferred to the particles of the string. As the wave travels, it produces a force that causes the particles to move up and down, creating a displacement.

3. How is displacement measured in a transverse wave on a string?

Displacement in a transverse wave on a string is typically measured in meters (m). It can be measured by observing the distance between the highest and lowest points of the wave, also known as the amplitude.

4. How does the amplitude affect the displacement of a transverse wave on a string?

The amplitude of a transverse wave on a string directly affects the displacement of the particles on the string. A larger amplitude results in a greater displacement, while a smaller amplitude results in a smaller displacement. This is because the amplitude represents the maximum displacement of the particles from their resting position.

5. How does the frequency of a transverse wave on a string affect its displacement?

The frequency of a transverse wave on a string does not directly affect its displacement. However, it does affect the wavelength and speed of the wave, which can indirectly impact the displacement. A higher frequency results in a shorter wavelength and faster speed, which can lead to a larger displacement of particles on the string.

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