# Waves - Multiple Choice Questions

Q1. Two points on a progressive wave are one-eighth of a wavelength apart.

The distance between them is 0.5 m, and the frequency of the oscillation is 10 Hz.

What is the minimum speed of the wave?

 A 0.2 m s−1 B 10 m s−1 C 20 m s−1 D 40 m s−1

λ = 8 x 0.5m = 4.0 m

c =

c = 4.0 x 10 = 40 m s−1

Q2. Which of the following waves cannot be polarised?

 A radio B ultrasonic C microwave D ultraviolet

Sound waves are longitudinal and cannot be polarised the others are transverse electromagnetic waves.

Q3. Which of the following is correct for a stationary wave?

 A Between two nodes the amplitude of the wave is constant. B The two waves producing the stationary wave must always be 180° out of phase. C The separation of the nodes for the second harmonic is double the separation of nodes for the first harmonic. D Between two nodes all parts of the wave vibrate in phase.

Q4. Sound waves cross a boundary between two media X and Y.

The frequency of the waves in X is 400Hz.

The speed of the waves in X is 330 ms −1 and the speed of the waves in Y is 1320 ms –1 .

What are the correct frequency and wavelength in Y?

 Frequency / Hz Wavelength / m A 100 0.82 B 400 0.82 C 400 3.3 D 1600 3.3

Frequency does not change when the wave passes into another medium.

c =

λ =c/f

λ = 1320 /400 = 3.3 m

Q5. What is the phase difference between two points 0.16 m apart on a progressive sound wave of frequency 256 Hz?

speed of sound = 330 m s–1

 A π/8 B π/6 C π/4 D π/3

speed =

λ = 330/256

λ = 1.29 m

0.16/1.29 = 0.124 ≈ 1/8th

2π/8 = π/4

Q6. The frequency of the first harmonic of a standing wave on a wire is f.

The length of the wire and tension in the wire are both doubled.

What is the frequency of the first harmonic as a result?

 A f/√2 B f C √2f D 2f

doubling the length halves the frequency

doubling the tension increases it by √2

overall effect = √2/2

but 2 = √2 x √2

so, overall effect = √2/(√2√2)

= 1/√2

Choice A

Q7. The graph below shows how the vertical height of a travelling wave varies with distance along the path of the wave.

The speed of the wave is 20 cm s–1. What is the period of the wave?

wavelength λ = 4 cm (see graph)

speed v = fλ

f = v/λ

f = 20/4 = 5 Hz

T = 1/f

T = 1/5 = 0.2 s

Choice B

 A 0.1 s B 0.2 s C 5.0 s D 10.0 s

Q8. Which statement is not correct for ultrasound and X-rays?

 A Both can be refracted B Both can be diffracted C Both can be polarised D Both can be reflected

Only transverse waves can be polarised - ultrasound is longitudinal - so it cannot be polarised - whereas X-rays are transverse.

Q9. A stationary wave is set up on a stretched string of length l and diameter d.

Another stationary wave is also set up on a second string made from the same material and with the same tension as the first.

What length and diameter are required for the second string so that both strings have the same first-harmonic frequency?

linear density μ = m/L

Volume V = L x ¼πd2

density ρ = m/V

so, ρ = m/(Lπd2)

and, m = ρLπd2

Substituting into μ = m/L we get:

μ =  ρLπd2/L = ρπd2

∴ f ∝ 1/L

and as f ∝ √μ but μ∝ d2

f ∝ d

So if diameter doubles length must halve - choice C

 Length of second string Diameter of second string A 2l 2d B l 2d C ½ l 2d D l ½d

Q10. A uniform wire, fixed at both ends, is plucked in the middle so that it vibrates at the first harmonic as shown.

What is the phase difference between the oscillations of the particles at P and Q?

Q11. Which row correctly shows electromagnetic radiations in order of decreasing wavelength?

 A gamma > ultraviolet > microwave B ultraviolet > gamma > microwave C microwave > ultraviolet > gamma D gamma > microwave > ultraviolet

decreasing wavelength - biggest wavelength first - so microwave as starter

Rather GCSE level this one!

Q12. Which statement is correct about the properties of an unpolarised electromagnetic wave as it passes through a polariser?

 A The wave remains unchanged B The wave does not pass through the polariser. C The wave’s electric field oscillates along the direction of travel. D The intensity of the wave is reduced.

The polariser absorbs all waves that are not in the direction of the polarising grid placed in its path. This removes some of the waves from the total, reducing the intensity.