For a harmonic wave given by determine (a) wavelength; (b) frequency; (c) propagation constant; (d) angular frequency; (e) period; (f) velocity; (g) amplitude.

For a harmonic wave given by y = (10 cm) sin[(628.3/cm)x − (6283/s)t]

determine (a) wavelength; (b) frequency; (c) propagation constant; (d) angular frequency; (e) period; (f) velocity; (g) amplitude.

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(a)  wavelength = 0.01m

(b) frequency = 999.84Hz

(c) propagation constant =  628.3/cm

(d) angular frequency = 6283/s

(e) period = 0.001s

(f) velocity = 9.9984m/s

(g) amplitude = 10cm

The general equation of a simple harmonic wave motion is given by;

y(x, t) = A sin (kx ± wt)           (i)

where;

y = vertical displacement

A = Amplitude

k = wave number = 2 π /  λ   [λ = wavelength]

w = angular velocity = 2π / T or  2πf  [T = period of oscillation, f = frequency]

t = time taken for displacement

x = horizontal displacement

The given equation is;

y = (10 cm) sin[(628.3/cm)x − (6283/s)t]        (ii)

Comparing the equations (i) and (ii)

y(x, t) = A sin (kx ± wt)           (i)

y = (10 cm) sin[(628.3/cm)x − (6283/s)t]        (ii)  

From comparison;

A = 10cm

k = 628.3/cm

w = 6283/s

(a) To calculate the wavelength, λ, we use the wave number relation as follows;

k = 2 π /  λ    (iii)

Where;

k = 628.3/cm

Substitute k = 628.3/cm into equation (iii) as follows;

628.3 = 2π / λ       [Take π = 3.142]

Solve for λ;

λ = 2(3.142) / 628.3

λ = 6.284 / 628.3

λ = 0.01m

Therefore the wavelength is 0.01m

(b) To calculate the frequency, f, we use;

w = 2π f          (iv)

where;

w = 6283/s

Substitute w = 6283/s into equation (iv) as follows;

6283 = 2 π f           [Take π = 3.142]

Solve for f;

f = 6283 / (2 π)

f = 6283 / (2 x 3.142)

f = 6283 / (6.284)

f = 999.84 Hz

Therefore, the frequency is 999.84 Hz

(c) The propagation constant is also called the wave number k.

As shown in the comparison of equations i and ii,

k = 628.3/cm

(d) The angular velocity, w = 6283/s     [as shown in the comparison of equations i and ii]

(e) To calculate the period, T, we use;

T = 1 / f       (v)

i.e the inverse of the frequency gives the period

Where;

f = 999.84 Hz

Substitute f = 999.84Hz into equation (v)

T = 1 / 999.84

T = 0.001 s

Therefore the period is 0.001 s

(f) The velocity, v, is the product of the wavelength (λ) and the frequency (f) as follows;

v = f x λ

Where;

f = 999.84 Hz

λ = 0.01m

Substitute these values into equation (vi) as follows;

v = 999.84 x 0.01

v = 9.9984m/s

Therefore, the velocity is 9.9984m/s

(g) The amplitude, A, is 10cm as shown in the comparison of equations (i) and (ii).

a.metals can become magnetic if they have many spinning electrons that create magnetic fields.d.only some metals are attracted by magnets; these metals are called ferromagnetic.

d.wrapping an insulated wire around a metal with ferromagnetic properties and applying an electric current.