eWave in the form y f (x,t) Find the maximum transverse velocity. b. 2. A transv

Question

eWave in the form y f (x,t) Find the maximum transverse velocity. b. 2. A transverse wave traveling along a string 2.0 meters long is described by tho equation: y 8.0 sin (.04 x-329. ere y and x are in centimeters and t in seconds. The mass of the stfing is 0.04 kg. a. Find the tension in the string b. If the string is held fixed at both ends would a standing wave result? How a. A steel piano wire 50 cm long, of mass 5 gm, is stretched with a tension of b. An open organ pipe (open at both ends) has a length of 9 meters. What is many loops? 400 N. What is the frequency of its fundamental mode of vibration? the fundamental frequency? , lesdot one endl is 220 cos. What i

Explanation / Answer

2)

compare the given equatio with y = A*sin(k*x - w*t)

so,

k = pi*0.04 rad/m

w = pi*32 rad/s

mass per unit length, mue = m/L = 0.04/2 = 0.02 kg/m

wave speed, v = w/k = pi*32/(pi*4)

= 8 m/s

we know,

sqrt(T/mue) = v

sqrt(T/mue) = pi*32/(pi*0.04)

T/mue = (32/4)^2

T = 64*mue

= 64*0.02

= 1.28 N

b) f = w/(2*pi)

= 32*pi/(2*pi)

= 16 hz

we know,

f = n*v/(2*L)

n = f*2*L/v

= 16*2*2*/8

= 8 loops

a) linear mass density, mue = m/L = 0.005/0.5 = 0.01 kg/m

wave speed, v = sqrt(T/mue)

= sqrt(400/0.01)

= 200 m/s

fundamental frequency, f = v/(2*L)

= 200/(2*0.5)

= 200 Hz

b)

fundamental frequency of open pipe, f = v/(2*L)

= 340/(2*9)

= 19 hz

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