1.A wave on a string is described by the relation y = A sin(45 t - 0.028 x ), wh

Question

1.A wave on a string is described by the relation y = A sin(45t - 0.028x), where t is measured in seconds and x in meters, with A = 0.14 m.
Find the frequency of the wave

Find the wavelength of the wave.

Find the speed of the wave.

2..Consider a wave that has a frequency of 6.1 kHz and a wavelength of 0.11 m. Write an equation that might describe this wave. (Assume that the amplitude is 1 m and the wave propagates in the positive x direction. Use the following as necessary: x, t, and ?.)

y(x,t)=?

3.The speed of a wave on a guitar string is v = 122 m/s. If the tension is increased from 63 N to 100 N, what is the new value of v?

Explanation / Answer

a)w = 2*pi*f =45

so frequency = 45/2pi = 7.16 Hz

2pi/lambda= 0.028

so lambda = 224.28 m

speed of wave = f* lambda = 224.28*7.16 = 16.5.84 m/s

b) w= 2*pi*f = 2 *3.14* 6.1 =38.308

2*pi/lambda = 2*3.14/0.11 = 57.09

so y (x,t) = 1 * sin (38.308t-57.09x)

c) velocity is directly proportional to squareroot of tension

v' = v * sqrt (100/63)

v' = 153.70 m/s

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