Waves — Numerical Practice
Covers: v = fλ, refractive index (n = sin i/sin r, n = 1/sin c), and sound speed via echoes and sonar. 20 questions.
A. Wave Speed (v = fλ)
A wave has a frequency of 50 Hz and a wavelength of 4 m. Calculate its speed.
A wave travels at 340 m/s with a wavelength of 0.5 m. Calculate its frequency.
Light travels at 3 × 10⁸ m/s with a frequency of 5 × 10¹⁴ Hz. Calculate its wavelength.
A wave has a period of 0.02 s. Calculate its frequency, then calculate its wavelength if its speed is 15 m/s.
Water waves in a ripple tank have a wavelength of 3 cm and a frequency of 4 Hz. Calculate their speed.
A sound wave of frequency 440 Hz travels at 340 m/s. Calculate its wavelength.
B. Refraction and Refractive Index
Light travels from air into glass with an angle of incidence of 60° and an angle of refraction of 35°. Calculate the refractive index of the glass.
A material has a refractive index of 1.5. Light hits it from air at an angle of incidence of 40°. Calculate the angle of refraction.
A material has a critical angle of 42°. Calculate its refractive index.
Water has a refractive index of 1.33. Calculate its critical angle.
Light inside glass (refractive index 1.5) hits the glass-air boundary at an angle of incidence of 50°. Calculate the critical angle, and hence explain what happens to the light.
Explain why the refractive index for light travelling from air into a denser medium is always greater than 1.
C. Sound Speed, Echoes and Sonar
A person claps 200 m from a wall and hears the echo 1.2 s later. Calculate the speed of sound.
The speed of sound in air is 340 m/s. Calculate the distance to a wall if an echo takes 0.5 s to return.
A ship’s sonar pulse returns after 0.8 s. The speed of sound in water is 1500 m/s. Calculate the depth of water beneath the ship.
A sonar signal takes 3 s to return from a seabed 2250 m deep. Calculate the speed of sound in water.
Explain why ultrasound, rather than audible sound, is used for medical scanning.
A submarine sends a sonar pulse and receives the echo 4 s later, from a target 3000 m away. Calculate the speed of sound in water.
State the approximate range of frequencies audible to the human ear, and define ultrasound.
An echo sounder on a boat records a return time of 0.04 s for a pulse sent to the seabed just below, where sound travels at 1450 m/s. Calculate the depth of the water.
Mastery Test
A wave has a frequency of 25 Hz and a wavelength of 8 m. Calculate its speed.
Sound travels at 1500 m/s in water with a wavelength of 0.3 m. Calculate the frequency.
Light hits a material with an angle of incidence of 50° and an angle of refraction of 30°. Calculate the refractive index.
A material has a refractive index of 1.4. Calculate its critical angle.
A person claps 150 m from a wall and hears the echo 0.9 s later. Calculate the speed of sound.
A sonar pulse in water (speed 1500 m/s) returns after 2.4 s. Calculate the depth.
State what determines the pitch of a musical note.
A wave has a period of 0.005 s. Calculate its frequency.
Explain why sound cannot travel through a vacuum.
Light of wavelength 5 × 10⁻⁷ m travels at 3 × 10⁸ m/s. Calculate its frequency.
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