Calculating Transverse Acceleration in Waves and Tension

[Soaring Crane]

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.

 

[Soaring Crane]

Could anyone give me any hints for #1?

Thanks again.

 

[OlderDan]

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.