y ( x,t ) = (1.90 cm) sin[(180 rad/s) t + (28 rad/m) x ] (select)particles in th

Question

y(x,t) = (1.90 cm) sin[(180 rad/s)t + (28 rad/m)x]

(select)particles in the airwave along the stringwave generator

A transverse wave on a string is described by the equation

y(x,t) = (1.90 cm) sin[(180 rad/s)t + (28 rad/m)x]

.

(a) What is the maximum transverse speed of a point on the string?

m/s

(b) What is the maximum transverse acceleration of a point on the string?

m/s2

(c) How fast does the wave move along the string?

m/s

(d) Why is your answer to (c) different from the answer to (a)?

The motion of the particles on the string is not the same as the motion of the

(select)particles in the airwave along the stringwave generator

.

Explanation / Answer

a)The max transverse speed will be:

v(max) = A w

v(max) = 1.9 x 10^-2 x 180 = 3.42 m/s

Hence, v(max) = 3.42 m/s

b)acc will be:

a(max) = A w^2

a(max) = 1.9 x 10^-2 (180)^2 = 615.6 m/s^2

Hence, a(max) = 615.6 m/s^2

c)k = 28 rad/m = 2 pi/lambda

lambda = 2 pi/28 = 0.22 m

180 = 2 pi f => f = 180/2 pi = 28.66 Hz

v = f lambda = 28.66 x 0.22 = 6.31 m/s

Hence, v = 6.31 m/s

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