A standing-wave pattern is observed in a thin wire with a length of 4.00 m. The wave function is y = 0.002 00 sin (πx) cos (100πt) where x and y are in meters and t is in seconds. (a) How many loops does this pattern exhibit? (b) What is the fundamental frequency of vibration of the wire?

A string oscillates according to the equation y' = (0.752 cm) sin[(7/5.0 cm-1)x] cos[(29.6 t s )t]. What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 1.74 cm when t = 1.17 s? (a) Number Units (b) Number Units (c) Number Units (d) Number i Units

13:35 O A O P A 1 99% A wave pulse travels down a slinky. The mass of the slinky is m = 0.89 kg and is initially stretched to a length L = 7.1 m. The wave pulse has an amplitude of A = 0.2 m and takes t = 0.426 s to travel down the stretched length of the slinky. The frequency of the wave pulse is f = 0.48 Hz. 1) What is the speed of the wave pulse? m/s Submit 2) What is the tension in the slinky? N Submit 3) What is the average speed of a piece of the slinky as a complete wave pulse passes? m/s Subrmit 4) What is the wavelength of the wave pulse? m Submit a 5) Now the slinky is stretched to twice its length (but the total mass does not change). What is the new tension in the slinky? (assume the slinky acts as a spring that obeys Hooke's Law) N Submit 6) What is the new mass density of the slinky? kg/m Subrmit " What is the new time it takes for a wave pulse to travel down the slinky? s Submit O 8) If the new wave pulse has the same frequency, what is the new wavelength? m Submit What…

A periodic vibration at x = 0, t = 0 displaces air molecules along the x direction by smax = 3.2E-05 m. The motion produces a sound wave that travels at a velocity of v = 336 m/s with a frequency of f = 120 Hz. Take the density of air as ρa = 1.20 kg/m3. Calculate the wavelength λ of the sound wave, in meters.  Calculate the wavenumber k of the sound, in radians per meter.  Calculate the angular frequency of the sound ω, in radians per second.

A piano wire with mass 2.60g and length 81.0cm is stretched with a tension of 30.0N . A wave with frequency 110 Hz and amplitude 1.40 mm travels along the wire. (a)Calculate the average power carried by the wave. (b)What happens to the average power if the wave amplitude is halved?

A string of mass 16.6 grams and length 0.74 meters and fixed at the ends is under tension 243 N. What is the vibrational frequency of n= 4 harmonic?

Take mx′′ + cx′ + kx = F0 cos(ωt). Fix m > 0, k > 0, and F0 > 0. Consider the function C(ω). For what values of c (solve in terms of m, k, and F0) will there be no practical resonance (that is, for what values of c is there no maximum of C(ω) for ω > 0)?

Hello, Can I please have help regarding this problem ? Thanks.    Suppose that the clock on our lecture room has a minute-hand length of 10 cm.(Use a coordinate system with the origin at center of clock and +x axis along the3PM direction and the +y direction along the 12PM direction). From the 12 to 8mark, for the tip of the minute hand:a) Sketch a vector diagram labeling ri, rf, Δr, Vi, Vf, and ΔV.b) Calculate the displacement vector in unit-vector notation.c) Calculate the average velocity vector in unit-vector notation.d) Calculate the average acceleration vector in unit-vector notation.e) Calculate magnitude and direction of the average acceleration vector.f) Calculate the magnitude and direction of the total acceleration of the tip ofthe minute hand at the 6 mark.