What is a vibrational frequency of the n=6 harmonic of a string of length 0.71 m strung at the tension 27.6 N, if the string is made of steel (density 7700 kg/m3) and has a diameter of 0.00771 m?

The equation of a certain traveling transverse wave is y1 = 2 cos (200nt -0.05nx) where x and ·y are in cm and t is the time in seconds. 18.Find the transverse velocity of the vibration in y-direction, as a function of time. Hint: Take the partial derivative withrespect to t, treating x as a constant. a. Uy= -400 n sin 2n(l OOt - 0.025x) c. Uy= -0.05 sin 2n(l00t - 0.025x) b. Uy = -200 sin 2n(l OOt - 0.025x) d. Uy= -0.10 n sin 2n(l OOt - 0.025x)

A string with a mass ? = 8.00? and a length ? = 5.00 ? has one end attached to a wall; the other end is draped over a small, fixed pulley a distance ? = 4.00? from the wall and attached to a hanging object with a mass ? = 4.00?? as shown in the figure. If the horizontal part of the string is plucked, what is the fundamental frequency of its vibration?

A simple pendulum is made of a 2 m-string and a bob of mass m. At t = 0, the pendulum is at its equilibrium position and is given an initial velocityv = 0.2 m/s. The maximum angular speed, 6'max, is: 0.8 rad/s 00.05 rad/s C 0.2 rad/s (:0.1 rad/s 0.4 rad/s A traveling wave on a taut string with a tension foreeTis given by the waye O O O

The height of the speaker stack was designed to be equal to the wavelength of the sound wave produced by the lowest string.    If the frequency of this harmonic vibration is 31 Hz and the length of the string is 0.89m (89cm), what is the speed of the ave on the string?    If the density of the string is 0.0657 kg/m what is the Tension of the string?    If the speed of sound is 343 m/s what will be the wavelength of the sound made by the first harmonic vibration (hint: this is the height of the tallest stack of speakers)

As shown in the figure, a plane simple harmonic propagates in the positive direction of the x-axis. Knowing that the vibration equation of point Py = Acos(wt+6) is the expression of the wave is U P X OA y = Acos{ w[t] + ] +0} - B. y = Acos { w[t_*+¹] +9} OC y = Acos{ w[t+¹=1+ø} D y = Acos { w[t+*+¹1+0} U

(a) Plot y versus t at x = 0 for a sinusoidal wave of the form y = 0.150 cos (15.7x - 50.3t), where x and y are in meters and t is in seconds. (b) Determine the period of vibration.

One end of a horizontal string is attached to a small- amplitude mechanical 60.0-Hz oscillator. The string's mass per unit length is 3.2 x10-4kg/m. The string passes over a pulley, a distance l = 1.50 m away, and weights are hung from this end. Assume the string at the oscillator is a node, which is nearly true. (Figure 1) Figure Oscillator -1.50 m 1 of 1 m What mass m must be hung from this end of the string to produce one loop of a standing wave? Express your answer to two significant figures and include the appropriate units. m1 = Submit Part B m2 = μA Value O Request Answer What mass m must be hung from this end of the string to produce two loops of a standing wave? Express your answer to two significant figures and include the appropriate units. μA Units Value ? Units ?

Consider the case of normal modes of vibration for the air column with only one end closed. What is the length of the air column for the fundamental harmonic? a) λ/2 b) λ c) 2λ d) λ/4

A piano tuner stretches a steel piano wire with a tension of 700 N. The steel wire is 0.425 m long and has a mass of 3.18 grams. What is the frequency (f) of its fundamental mode of vibration? (Hint: The linear mass density, ?, is the amount of mass per unit length which is measured in kg/m. To compute it, just divide the mass and the length of the material.)