Calculating Transverse Acceleration in Waves and Tension

In summary, two conversations were had regarding a wire under tension with specified parameters such as length, mass, and wave properties. In the first conversation, the maximum transverse acceleration of a point on the wire was discussed, with options for possible values. In the second conversation, the time for a crest of the wave to travel the wire's length was being calculated. Hints were sought for solving these problems involving harmonic motion.
  • #1
Soaring Crane
469
0
1) A wire, 7.0 m long with a mass of 50 g, is under tension. A traverse wave is propagated on the wire, for which the frequency is 160 Hz, the wavelength is .60 m, and the amplitude is 2.1 mm. The maximum transverse acceleration, of a point on the wire, in SI units is closest to:

a. 1600-------b.1300--c.1900-----d.2100------e.2400

Exactly what is the transverse acceleration in theory/formula? I know that partial derivatives are involved, but I don't understand how to use partial differentiation. Any hints for this problem are appreciated.




2) A wire, 2.0 m long, with mass of 40 g, is under tension. A transverse wave is propagated on the wire, for which the frequency is 330 Hz, wavelength is 0.50 m, and amplitude is 2.9 mm. The time, for a crest of the wave to travel the wire's length, in ms, is closest to:

a. 15------b. 12-----c. 16----d. 11----e. 14


v = sqrt(F_T/(m/L))
m = 0.04 kg
L = 2.0 m

F_T = 9.8 m/s^2*0.04 kg

v = sqrt[F_T/(0.04 kg/2.0 m)] = 4.4272 m/s

f = 4.27 m/s/0.50 m = 8.54 1/s

T = 1/8.54 s^-1 = 0.1172 s*(1000 ms/s) = 117.2 s

Now I am lost. How do I find the time for the crest with the amplitude and frequency?

Thanks.
 
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  • #2
Could anyone give me any hints for #1?

Thanks again.
 
  • #3
Soaring Crane said:
Could anyone give me any hints for #1?

Thanks again.

The wave has a specified frequency, so you know the wave is harmonic. Each point on the string is moving perpendicular to the length of the string (transversely) in harmonic motion with the wave frequency and wave amplitude. Relate this to what you know about the motion of any harmonic oscillator.
 

Related to Calculating Transverse Acceleration in Waves and Tension

1. How do you calculate transverse acceleration in waves and tension?

In order to calculate transverse acceleration in waves and tension, you will need to use the formula: a = (T/m) * sin(theta), where a is the acceleration, T is the tension, m is the mass of the object, and theta is the angle of the wave.

2. What is the relationship between transverse acceleration and tension in waves?

The transverse acceleration of an object in a wave is directly proportional to the tension in the wave. This means that as the tension increases, the transverse acceleration also increases.

3. How does the mass of an object affect transverse acceleration in waves?

The mass of an object has an inverse relationship with the transverse acceleration in waves. This means that as the mass increases, the transverse acceleration decreases.

4. Can you calculate transverse acceleration without knowing the tension in the wave?

No, in order to calculate transverse acceleration, you will need to know the tension in the wave as well as the mass and angle of the wave. Without knowing the tension, it is not possible to accurately calculate the transverse acceleration.

5. What is the significance of calculating transverse acceleration in waves and tension?

Calculating transverse acceleration in waves and tension allows us to understand how an object will move in a wave and how different factors, such as tension and mass, will affect its movement. This information is important in various fields, such as marine engineering, oceanography, and even sports like surfing and sailing.

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