A guitar string is vibrating in its fundamental mode, with nodes ateach end. The length of the segment of the string that is free tovibrate is 0.380 m. The maximum transverse acceleration of a pointat the middle of the segment is 8300 m/s^2 and the maximumtransverse velocity is 3.10 m/s.

What is the amplitude of this standing wave?

What is the wave speed for the transverse traveling waves on thisstring?

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A string of length (L) and mass (M) vibrating with a linearfrequency (f) and amplitude (A) has a periodic transversedisturbance traveling its length at a speed (v).

L = 2.00 meters = length of string
M = 0.005 kg = mass of string
f = 100 Hz = linear frequency of vibration
A = 0.030 meters = amplitude of the period transverse wavetraveling in the string
v = 20 m/s = speed of the transverse wave traveling down thestring

Determine the following:
a) Wavelength of the periodic disturbance
b) Wave number
c) Tension in the string
d) Fundamental frequency in the string
e) Maximum transverse speed and maximum transverse acceleration ofany small bit of string
f) Displacement of the bit of string at x = L/4 when t = 0.5seconds
g) Speed of the bit of string at x = 3L/4 when t = (1/80)seconds
h) Average total energy of waves on the string
i) Average rate at which energy is transmitted along the string

A thin string 2.50 m in length is stretched with a tension of 90.0 N between two supports. When the string vibrates in its first overtone, a point at an antinode of the standing wave on the string has an amplitude of 3.50 cm and a maximum transverse speed of 28.0 m/s. (a) What is the string’s mass? (b) What is the magnitude of the maximum transverse acceleration of this point on the string?

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A light 3 m long string with a mass per unit length of 8.00 gm/mhas its ends tied to two walls separated by a distance equal to 3/4the length of the string. An object of mass M is suspended from thecenter of the string, putting tension in the string.

a) Determine an expression for the transverse wave speed in thestring as a function of the mass of the hanging object.

b) What should be the mass of the object suspended from thestring if the wave speed is to be 60.0m/s?

c) If the wave speed is 60.0 m/s and you pluck the string andobserve that it is vibrating in the simplest possible mode, what isthe wavelength and frequency of the transverse wave in thestring?

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