Explain what is meant by a progressive transverse wave.

Question 8

(a) (i) Explain what is meant by a progressive transverse wave.  [2]

(ii) Define frequency. [1]

(b) The variation with distance x of displacement y for a transverse wave is shown in Fig. 7.1.

Fig. 7.1

On Fig. 7.1, five points are labelled. Use Fig. 7.1 to state any two points having a phase difference of

(i) zero, [1]

(ii) 270°. [1]

 (c) The frequency of the wave in (b) is 15 Hz. Calculate the speed of the wave in (b). [3]

(d) Two waves of the same frequency have amplitudes 1.4 cm and 2.1 cm.

Calculate the ratio

intensity of wave of amplitude 1.4 cm
intensity of wave of amplitude 2.1 cm

[2]

Reference: Past Exam Paper – November 2014 Paper 23 Q7

Solution:

(a) (i) A progressive transverse wave is a wave in which energy is transferred from one place to another (without the bulk movement of the medium) with the vibration of the particles being at right angles to the direction of travel of the energy.

(ii) Frequency is defined as the number of oscillations per unit time / number of wavefronts passing a point per unit time.

(b)

(i)

P and T

{A phase difference of zero means that the points are in phase. These points are separated by a distance equal to the wavelength. i.e. two crests, two troughs …}

(ii)

P and S           or Q and T

{The difference between point P and T gives the wavelength (= 1.8 – 0.6 = 1.2 cm). This corresponds to a phase difference of 360° or zero.

360° - - - > 1.2 cm

1° - - - > 1.2 / 360

270° - - - > 1.2 × 270 / 360 = 0.9 cm

So, points having a phase difference of 270° are separated by a distance of 0.9 cm.}

 (c)

Wavelength λ = 1.2×10^-2 (m)            

v = fλ

v = 15 ×1.2×10^-2                      

v = 0.18 m s^-1                                 

(d)

{The intensity is proportional to the square of the amplitude.}

ratio = (1.4)² / (2.1)²

ratio = 0.44