Question

A transverse, travelling wave on a chord is represented by = 0.22sin (5.6 + 34) where and are in meters and is in seconds. For this wave, determine; (a) Wavelength (b) Frequency (c) Velocity (both magnitude and direction) (d) Amplitude (e) Maximum and minimum speeds of particles on the chord.

Answer 1

Answer:

A)  1.122 m

B)  5.4 hertz

C)  6.06 m/s ( towards negative  x axis )

D)  0.22

E)  max speed = amplitude * 34

                  = 0.22 * 34 = 7.48

  minimum speed ( speed at rest ) = 0

Explanation:

The travelling wave = D = 0.22sin ( 5.6x + 34t)

this wave is represented in the form : D = Asin ( kx + wt)

A) wavelength

k = 2$\pi$ / v

v = wavelength

k = 5.6

therefore wavelength ( v ) from the equation = 2$\pi$ / 5.6 = 1.122 m

B ) frequency

w = 2$\pi$f

w = 34

f = frequency

therefore f = w / 2$\pi$  = 34 / 2$\pi$ = 5.4 hertz

C ) velocity

speed = f v

v = 5.4 * 1.122 = 6.06 m/s ( towards negative  x axis )

D) amplitude

A = 0.22

E ) maximum and minimum speeds of particles on the chord

max speed = amplitude * 34

                  = 0.22 * 34 = 7.48

minimum speed ( speed at rest ) = 0