Question

PITY263: Ch 16 Written Tomework, Due Thursday, Sept 12 at 8:00 am Note on homework solutions: In order to receive full credit for homework solutions, your work needs to be presented clearly, neatly, and completely. State answers to no more than three significant figures. 1. A sinusoidal transverse wave is traveling along a taut wire in the negative x-direction. It has an angular wave number of 1.50 cm-1, a period of 2.50 ms, and an amplitude of 35.0 mm, Take the transverse direction to be the y-direction (a) Write an equation describing the wave. (b) What is the maximum transverse speed of a point on the wire (in meters per second)? (c) If the cord is under a tension of 12.0 N, determine its lincar mass density (in grams per centimeter). 2. A string, tied to a sinusoidal oscillator at P and running over a support at Q. is put under tension by a block of mass m. The separation between P and Q is given by L = 0.850 m, the lincar density of the string is given by u = 1.40 g/m, and the oscillator frequency is set to f = 150 Hz. The amplitude of the motion at Pis small enough for that point to be considered a node. A node also exists at Q. Take the acceleration of gravity to be g = 9.8 m/s2 Oscillator (a) What mass m allows the oscillator to set up the fourth harmonic on the string? (Shown above) (b) For the mass found in part (a), to what frequency must the oscillator be adjusted to, to set up the first harmonic? (c) The string is swapped out for one whose linear mass density is four times that of the first string. Using the mass found in part (a) and the frequency found in part (b), what standing wave mode, if any, is set up in the string?

Detailed explantion please.

Answer 1

sinusoida eneral eguation of string t rave lling Wave on a direition is, =A sin (kxtwt) Here, A amplitude angalar angu lar freguency wave number iven A 35-0mm 0.035 m k= 50 cm 150 m Time petidd T= 2.50 ms x103 2 50 We have for mula 2 T 2513 T 2.5 x103 S equation 035) sin (usen +s1))

point C) (b transverse speed of be found by, can a Differentiate y relative =035)5) c150x COS +2513t is - Since maximum value of cosine maximum , is Co-035)(251) ая max 87.9 (Speed of wave found by propagation bwo formulae be Can Ftension cmd Klinear ma ss Дnity н 50 25133 w2 = 0. 0427 kg ting Conver M=0.0417) O.427