Mechanical sinusoidal transverse wave

In summary, the conversation revolved around solving for various properties of a sinusoidal transverse wave traveling along a string, including amplitude, wavelength, wave speed, period, maximum transverse speed, and phase angle. The main difficulty was converting units to find the correct values, but the participants were able to solve the problem with some guidance.
  • #1
NAkid
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0
[SOLVED] mechanical waves

Homework Statement


A sinusoidal transverse wave is traveling along a string in the negative direction of an x-axis. The figure shows a plot of the displacement as a function of position at time t=0; the y-intercept is 4.0m. The string tension is 6.8N, and its linear density is 47.22 g/m.

Find the amplitude (cm).
Find the wavelength (cm).
Find the wave speed (cm/s).
Find the period of the wave.
Find the maximum transverse speed of a particle in the string.
What is the phase angle in degrees?

Homework Equations





The Attempt at a Solution


So linear density is the mass per unit length. it's not in the units we want (kg/cm), so convert and get 4.722E-4 kg/cm.
wave speed = sqrt(T/wave length) = sqrt(6.8/4.722E-4), but this isn't the right answer. did i convert wrong?

also I'm having trouble finding the amplitude and wave length, probably for the same reason as above.
 

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  • #2
it is better to start from meter and kg, since N is in terms of these SI units. after calculation, you can always convert back to cm to give answers.
 
  • #3
ok, got that wavelength wave sped and period. what is the difference between wave speed and max transverse speed? also, I'm sure this is really obvious but i can't figure out the amplitude either
 
  • #4
never mind i got it, thanks
 

Related to Mechanical sinusoidal transverse wave

1. What is a mechanical sinusoidal transverse wave?

A mechanical sinusoidal transverse wave is a type of wave that travels through a medium by causing the particles of the medium to oscillate perpendicular to the direction of the wave's propagation. This type of wave is characterized by its sinusoidal shape, which is a smooth and repetitive curve resembling a wave.

2. What are some examples of mechanical sinusoidal transverse waves?

Some common examples of mechanical sinusoidal transverse waves include waves on a string, seismic waves, and water waves. Sound waves can also be considered mechanical sinusoidal transverse waves, but they require a medium to travel through and cannot propagate in a vacuum.

3. How do mechanical sinusoidal transverse waves differ from other types of waves?

Mechanical sinusoidal transverse waves differ from other types of waves in the way they transfer energy and the direction of particle motion. Unlike longitudinal waves, which cause particles to oscillate parallel to the direction of wave propagation, transverse waves cause particles to oscillate perpendicular to the direction of wave propagation.

4. What is the equation for the speed of a mechanical sinusoidal transverse wave?

The equation for the speed of a mechanical sinusoidal transverse wave is v = fλ, where v is the speed of the wave, f is the frequency, and λ is the wavelength. This equation is commonly known as the wave equation and is used to calculate the speed of any type of wave.

5. How are mechanical sinusoidal transverse waves measured and analyzed?

Mechanical sinusoidal transverse waves can be measured and analyzed using various tools and techniques, such as a wave analyzer or an oscilloscope. These tools can help scientists measure the wavelength, frequency, and amplitude of the wave, as well as its speed and direction of propagation. Additionally, mathematical models and simulations can also be used to analyze and predict the behavior of mechanical sinusoidal transverse waves.

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