These questions revise the lessons in waves. Use 340 m s⁻¹ for the speed of sound in air and 3.0 × 10⁸ m s⁻¹ for electromagnetic waves.
Try each question on paper first.
Questions
Question 1
Ten complete waves pass a point in 2.0 s, and the wavelength is 0.40 m. Find the frequency and the speed.
Answer
f = 10 ÷ 2.0 = 5.0 Hz. v = fλ = 5.0 × 0.40 = 2.0 m s⁻¹.
Question 2
A radio station broadcasts at 90 MHz. Find the wavelength of its waves.
Answer
90 MHz = 9.0 × 10⁷ Hz. λ = v ÷ f = 3.0 × 10⁸ ÷ 9.0 × 10⁷ = 3.3 m.
Question 3
Water waves of frequency 4.0 Hz travel at 0.24 m s⁻¹ in deep water and at 0.16 m s⁻¹ in shallow water. Find the wavelength in each region.
Answer
Deep: λ = 0.24 ÷ 4.0 = 0.060 m. Shallow: λ = 0.16 ÷ 4.0 = 0.040 m.
The frequency is 4.0 Hz in both regions, since the source has not changed.
Question 4
State one condition that makes diffraction of water waves through a gap more noticeable.
Answer
Make the gap narrower, so its width is closer to the wavelength (or smaller). A longer wavelength, from a lower frequency, also increases the spreading.
Question 5
Two speakers emit a note of wavelength 0.50 m in phase. A listener is 4.0 m from one and 5.25 m from the other. Is the sound loud or quiet?
Answer
Path difference = 5.25 − 4.0 = 1.25 m = 2.5λ. That is a whole number plus a half, so the interference is destructive and the sound is quiet.
Question 6
A double-slit experiment has slit separation 0.30 mm and a screen 1.5 m away. The bright fringes are 3.0 mm apart. Find the wavelength.
Answer
λ = ax ÷ D = (0.30 × 10⁻³ × 3.0 × 10⁻³) ÷ 1.5 = 9.0 × 10⁻⁷ ÷ 1.5 = 6.0 × 10⁻⁷ m.
Question 7
A sonar pulse returns from a shoal of fish after 0.060 s. The speed of sound in water is 1500 m s⁻¹. How deep are the fish?
Answer
Down and back: 1500 × 0.060 = 90 m. The depth is 90 ÷ 2 = 45 m.
Question 8
A displacement-time graph shows 5 complete cycles in 2.0 s. A displacement-distance graph for the same wave shows a wavelength of 0.80 m. Find the wave speed.
Answer
T = 2.0 ÷ 5 = 0.40 s, so f = 2.5 Hz. v = fλ = 2.5 × 0.80 = 2.0 m s⁻¹.
The wavelength came from the distance graph and the period from the time graph.
If you got these wrong
Question 1 to 2 need relating speed, frequency and wavelength. Questions 3 and 4 need explaining reflection, refraction and diffraction.
Questions 5 and 6 need reading interference patterns. Question 7 needs comparing sound and electromagnetic waves, and question 8 needs interpreting wave graphs.
To work through your wrong answers with a teacher, see online one-to-one Physics tuition.