Introduction to waves: 10. WAVE CALCULATIONS - formulae and how to solve wave problem questions

Doc Brown's Physics exam study revision notes

Q1 A wave has a speed of 0.25 m/s and a wavelength of 5.0 cm.

(a) Calculate the frequency of the wave

f = v ÷ λ 

5.0 cm ≡ 5/100 m = 0.05 m

Therefore frequency = 0.25/0.05 = 5.0 Hz

(b) Calculate the period of the wave.

period = 1 / frequency = 1 / 5 = 0.20 s

Q2 The frequency of sound in air at room temperature and pressure is 343 m/s.

The musical note middle C has a frequency of 262 Hz.

Calculate the wavelength of the middle C sound.

λ = v ÷ f

wavelength = 343 ÷ 262 = 1.31 m (131 cm, 3 s.f.)

 

Q3 A set of ocean waves has a frequency of 0.50 Hz.

If the average distance between the crests of the waves is 10 m, what is the average speed of the ocean waves?

 v = f x λ

speed (m/s) = frequency (Hz) x wavelength (m)

speed = 0.5 x 10 = 5.0 m/s

Q4 The time period of a radio electromagnetic wave is 5.0 x 10^-5 seconds

(a) What is the frequency of the radio wave?

period = 1 / frequency

f = 1 / period = 1 / (5.0 x 10^-5) = 2.0 x 10⁴ Hz

(b) If the 'speed of light' is 3.0 x 10⁸ m/s, calculate the wavelength of the radio wave in m.

λ = v ÷ f = 3.0 x 10⁸ / 2 x 10⁴ = 1.5 x 10⁴ m

(c) If the distance from the radio station to your radio is 200 km, how long does it take the signal to reach you?

The speed formula is v = d / t,  so  t = d / v = (200 x 1000) / (3.0 x 10⁸) = 6.7 x 10^-4 s

Q5 A water wave has a frequency of 0.50 Hz and a wavelength of 150 cm.

(a) Calculate the speed of the wave in m/s.

 v = f x λ = 0.50 x (150/100) = 0.075 m/s

(b) If the frequency of this wave triples, what will be its wavelength? and what assumption have you made?

If you assume the speed stays the same, the wavelength will be a third of 150 cm, 50 cm or 0.50 m,

because frequency x wavelength (f x λ) is a constant for a constant speed.

(c) If the frequency of the original wave doubles, and the wavelength of the wave quadruples, what will be the new speed of the wave?

v = f x λ, putting in the factors gives 2 x (1/4) = 0.5, so the new speed will be 0.5 x 0.075 = 0.038 m/s  (2 sf)

 

Q6 Suppose an airliner sends out a microwave radar signal of wavelength of 1.20 cm.

The microwave reflects off another aircraft and the echo is detected after a time lapse of 6.0 µs.

The speed of electromagnetic radiation = 3.00 x 10⁸ m/s.

(a) What is the frequency of the microwave beam?

speed = wavelength x frequency

f = v ÷ λ = 3.00 x 10⁸ ÷ (1.20 / 100) = 2.50 x 10¹⁰ Hz

(b) What is the distance between the two aircraft?

s = d / t,  d = s x t = 3.00 x 10⁸ x 6.0 x 10^-6 = 1800 m (total distance including echo)

distance between aircraft = 1800 ÷ 2 = 900 m

(µ is micro = 10^-6, and total distance is halved because it involves 'there and back')

Q7 A satellite is 75 km above the Earth's surface. (speed of light 3.00 x 10⁸ m/s)

What is the shortest time that a microwave signal would take to reach the satellite from the Earth's surface?

s = d / t,  t = d / s = (75 x 1000) / (3.00 x 10⁸) = 2.50 x 10^-4 seconds

Q8 A red light wave has a wavelength of 7.0 x 10^-7 m. (speed of light 3.00 x 10⁸ m/s)

What is the frequency of the light wave?

v = f x λ  *  f = v / λ  = 3 x 10⁸ / (7.0 x 10^-7 m) = 4.29 x 10¹⁴ Hz  (3 sf)

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