Exam-style Questions: Progressive Waves

1. Radio waves cannot be transmitted through water, but submarines can now transmit and receive e-mails, without having to surface. An 'accoustic modem' on the submarine transmits sound waves through water, at a frequency of 8.0 kHz, The waves carry information at 2.4 kbit s-1 to a radio buoy. The information is relayed from the buoy to shore by radio waves. The buoy can also receive radio signals, and transmit the information as sound waves back to the submarine.

a) Show that the wavelength of the 8.0 kHz sound waves in sea water is about 0.2 m.

speed of sound n sea water = 1500 m s-1

(3 Marks)

b) The sound waves travel 5.0 km from the submarine to the buoy.

Calculate the time taken for the sound waves to travel this distance.

time taken = ......................... s

(2 Marks)

(Marks available: 5)

2. This question is about a violin. Fig. 8.1 shows a violin with its four strings in place. Each string is in tension between the bridge X and the nut Y. At X and Y the mvoement of the strings is restricted.

Fig. 8.2 shows one of the four strings on the violin. a) Draw on Fig. 8.2 the lowest frequency standing wave that can be obtained on the string. Label the nodes and antinodes with the letters 'N' and 'A' respectively.

(2 Marks)

b) The length L of the string betweem X and Y is 0.40 m.

State the wavelength of the standing wave you have drawn.

wavelength = ............................. m

(1 Mark)

c) The frequency of the lowest frequency standing wave is 440 Hz.

Calculate the velocity v of the transverse waves on the string.

velocity = ....................... m s-1.

(2 Marks)

(Marks available: 5)

3. Fig. 3.1 represents the screen of a cathode ray oscilloscope (c.r.o.). The time-base setting is 0.50 ms cm-1 and the voltage (y-gain) setting is 2.0 mV cm-1. A microphone connected to the c.r.o. detects a pure (sinusoidal) sound wave note of frequency 500 Hz.

a) Calculate the period of the note.

period = ............................. s

(1 Mark)

b) The amplitude of the signal from the microphone produced by the note is 6.0 mV.

Draw on Fig. 3.1 the trace produced on the c.r.o. screen when the mircophone detects the sound wave. Draw at least two full cycles of the wave on Fig. 3.1.

(3 Marks)

c) The speed of sound in air is 330 m s-1. Calculate the wavelength of the sound received by the microphone.

wavelength = .................... m

(2 Marks)

(Marks available: 6)

Answer outline and marking scheme for question:

1. a) λ = v / f ; = 1500 / 8000 ; = 0.19 m

ora v = 1600 m s-1 is about 1500 m s -1 full marks

(3 Marks)

b) t = s / v / = 5000 / 1500 ; = 3.3 s

(2 Marks)

(Marks available: 5)

2. a) One loop (1 Mark) nodes and antinodes labelled (1 Mark)

(2 Marks)

b) 0.8 (m) (1 MArk) ecf from a)(i)

(1 Mark)

c) = 440 x 0.8 (1 Mark) = 352 (m s-1) (1 Mark) ecf from a)(ii)

(2 Marks)

(Marks available: 5)

3. a) period = 1/500 = 0.002s (or 2ms)

(1 Mark)

b) at least 2 full (sine) waves of constant period (+/- 2mm)

of amplitude 3 cm (+/- 2mm in both directions)

correct 'period' of 4 cm (+/- 2mm throughout)

(3 Marks)

c) correct substitution into v = f λ : e.g. 330 = 500 λ

λ = 0.66 m {do not allow 0.6 but allow 0.7 }

(2 Marks)

(Marks available: 6) 