A stretched string is fixed at both ends and made to vibrate with a frequency of 25 Hz. A stationary wave is formed on the string. The distance between the fixed ends of the string is 0.96 m.

Figure 5.1 shows the string at one instant.

Figure 5.1, a stationary wave on a string of length 0.96 m fixed at both ends, drawn with three antinodes in sequence between the fixed ends -- a loop above the line, then a loop below, then a loop above -- showing one and a half wavelengths, marked not to scale

5(b)(i)Standing WavesEasy1 mark

On Figure 5.1, draw a cross (

\times

) at the position of an antinode.

Draw with the mouse or a finger.

5(b)(ii)Standing WavesMedium3 marks

Show that the speed of a progressive wave on the string is 16 m s

^{- 1}

Answer

0 words

5(b)(iii)Standing WavesMedium2 marks

The frequency of the vibrations is increased to 30 Hz. The speed of the wave on the string does not change. State and explain whether a stationary wave is formed.

Answer

0 words

5(c)

A beam of light of wavelength

4.5 \times 1 0^{- 7}

m is incident normally on a diffraction grating with

6.7 \times 1 0^{5}

lines per metre. The light passes through the grating and forms a pattern of bright spots on a screen that is parallel to the grating.

Figure 5.2 shows two of the bright spots in the pattern.

Figure 5.2, a diffraction grating with a beam of light incident normally, forming a central bright spot straight ahead on a screen parallel to the grating and a second bright spot at position X; the angle between the central bright spot and X, measured at the grating, is 37 degrees, marked not to scale

The angle formed at the diffraction grating between the central bright spot and the bright spot at position X is

3 7^{\circ}

5(c)(i)Diffraction Diffraction GratingsMedium3 marks

Calculate the order

n

of the bright spot formed at X.

5(c)(ii)Diffraction Diffraction GratingsMedium1 mark

The diffraction grating is replaced by a grating with fewer lines per metre. State how this affects the distance between adjacent bright spots on the screen.