The equation of a transverse wave traveling along a very longstring is given by

Question

The equation of a transverse wave traveling along a very longstring is given by y = 6.0sin(0.027x +5.0t), wherex and y are expressed in centimeters andt is in seconds. Determine the following values. (a) the amplitude
1 cm

(b) the wavelength
2 cm

(c) the frequency
3 Hz

(d) the speed
4 cm/s

(e) the direction of propagation of the wave 5 +x
-x
+y
-y


(f) the maximum transverse speed of a particle in the string
6 cm/s

(g) the transverse displacement at x = 3.5 cm whent = 0.26 s
7 cm

Section 16-5 The Speed of a TravelingWave (a) the amplitude
1 cm

(b) the wavelength
2 cm

(c) the frequency
3 Hz

(d) the speed
4 cm/s

(e) the direction of propagation of the wave 5 +x
-x
+y
-y


(f) the maximum transverse speed of a particle in the string
6 cm/s

(g) the transverse displacement at x = 3.5 cm whent = 0.26 s
7 cm 5 +x
-x
+y
-y
5 +x
-x
+y
-y
5

Explanation / Answer

Given by y = 6.0sin(0.027x +5.0t), cmpare this with y = A sin ( kx + w t ) we get amplitude A= 6 cm propagation constant k = 0.027 So, wavelength = 2 / k                           = 74.074 cm angular frequency w = 5 So, frequency f = w / 2                          = 2.5 Hz speed v = w / k              = 185.185 cm / s wave travel in -y axis Maximum speed V = A w                              = 94.24 cm / s

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