Edexcel A-Level Physics: Waves and Particle Nature of Light

A guitar string is fixed rigidly at both ends and is plucked. A stationary (standing) wave is set up on the string, and at certain frequencies the string vibrates strongly to produce a clear musical note.

Explain how a stationary wave is formed on the string, and describe how the pattern of nodes and antinodes changes as the string vibrates in its first harmonic (fundamental) and then in its second harmonic. In your answer you should refer to superposition, the phase relationship of the waves that meet, and why only certain frequencies produce a strong vibration.

(6 marks)

Monochromatic light from a sodium lamp is passed normally through a diffraction grating that has 500 lines per millimetre. The diffraction pattern is observed on a screen.

Quantity	Value
Number of lines per millimetre	500 mm⁻¹
Wavelength of the light, $\lambda$λ	589 nm

(a) Show that the grating spacing $d$d (the distance between adjacent slits) is $2.00 \times 10^{-6}$2.00×10−6 m. (1 mark)

(b) Calculate the angle, measured from the straight-through direction, at which the first-order maximum is seen. (2 marks)

(c) Determine the highest order of maximum that can be observed with this grating and light. (3 marks)

A string is stretched between two fixed points 0.80 m apart and driven by a vibration generator. The driving frequency is slowly increased and the frequency at which each successive harmonic (stationary-wave mode) is observed is recorded:

Harmonic number, $n$n	1	2	3	4	5
Resonant frequency / Hz	150	300	460	600	750

The resonant frequencies of a string fixed at both ends are given by $f_n = \dfrac{nv}{2L}$fn​=2Lnv​, where $v$v is the speed of the waves on the string.

(a) State which one reading appears anomalous, giving a reason. (1 mark)

(b) Use the non-anomalous data to determine the speed of the waves on the string. (3 marks)

(c) Predict the frequency of the seventh harmonic. (1 mark)

A clean sodium surface has a work function of 2.28 eV. It is illuminated with monochromatic violet light of wavelength 400 nm, and photoelectrons are emitted.

Use $h = 6.63 \times 10^{-34}$h=6.63×10−34 J s, $c = 3.00 \times 10^8$c=3.00×108 m s⁻¹ and $e = 1.60 \times 10^{-19}$e=1.60×10−19 C.

(a) Calculate the maximum kinetic energy of the emitted photoelectrons, in joules. (3 marks)

(b) Calculate the longest wavelength of light (the threshold wavelength) that would still cause photoelectrons to be emitted from this surface. (2 marks)

In an electron-diffraction demonstration, electrons travel through a thin crystal whose atoms are spaced about $2 \times 10^{-10}$2×10−10 m apart, and a diffraction pattern is seen on a screen. Each electron moves with a speed of 2.00 × 10⁶ m s⁻¹.

Use $h = 6.63 \times 10^{-34}$h=6.63×10−34 J s and $m_e = 9.11 \times 10^{-31}$me​=9.11×10−31 kg.

(a) Calculate the de Broglie wavelength of one of these electrons. (3 marks)

(b) With reference to your answer, explain why a diffraction pattern is observed when the electrons pass through this crystal. (1 mark)

Total internal reflection inside optical fibres relies on the refractive index of the materials and on the critical angle.

(a) Define the absolute refractive index of a medium, writing down the defining equation and stating what each symbol represents. (2 marks)

(b) State the two conditions that must be satisfied for total internal reflection to occur at the boundary between two media. (1 mark)