Waves — Solutions
Full worked solutions, with method and final answer for every part.
Question 1
(a)v = fλ.
v = 50 × 0.06 = 3.0 m/s
Question 2
(a)Period T = time ÷ number of oscillations; frequency f = 1/T.
T = 2.0 ÷ 4 = 0.5 s, so f = 1 ÷ 0.5 = 2 Hz
Question 3
(a)The 0.5 s covers the round trip (down and back), so time one-way = 0.25 s. Depth = speed × time (one-way).
depth = 1500 × 0.25 = 375 m
Question 4
(a)In a transverse wave, particles vibrate perpendicular to the direction of energy transfer (e.g. light, water waves). In a longitudinal wave, particles vibrate parallel to (along) the direction of energy transfer (e.g. sound).
Transverse: vibration ⊥ travel direction (e.g. light). Longitudinal: vibration ∥ travel direction (e.g. sound)
Question 5
(a)T = 1/f.
1 ÷ 25 = 0.04 s
Question 6
(a)λ = v/f.
340 ÷ 170 = 2.0 m
Question 7
(a)λ = vT.
1500 × 0.002 = 3.0 m
Question 8
(a)The 0.8 s is a round trip, so the one-way time is 0.4 s. Depth = speed × time.
1500 × 0.4 = 600 m
Question 9
(a)Light is a transverse wave. A transverse wave can be polarised (vibrations restricted to one plane), which a longitudinal wave cannot.
Light is transverse; transverse waves can be polarised, longitudinal waves cannot
Question 10
(a)Since v = fλ and frequency is unchanged, a decrease in speed (entering a slower medium) must be matched by a proportional decrease in wavelength.
The wavelength decreases, in proportion to the decrease in speed
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