Relations used: v = fλ | T = 1/f | distance = speed × time | for an echo, sound travels to the reflector and back (2d).
1Which observation best supports the idea that sound is a mechanical wave?
Answer: (ii) Sound needs a medium to propagate
Mechanical waves travel through the vibration of particles of a medium. Sound cannot travel through vacuum.
2For a sound wave propagating in a medium, increasing its frequency will increase its
Answer: (iii) number of compressions per second
Frequency is the number of compressions (or rarefactions) passing a point per second. Speed stays the same in a medium, so wavelength and time period decrease.
3If 20 compressions pass a point in 4 seconds, the frequency is
f = 20/4 = 5 Hz
Answer: (ii) 5 Hz
4In a room, the reflected sound reaches the ear 0.05 s after its production. Will it produce an echo or reverberation? Justify your answer.
It will produce reverberation.
To hear an echo, the reflected sound must reach us at least 0.1 s after the original sound. Here the gap is only 0.05 s. So the reflected sound mixes with the original sound and makes it last longer.
5Graphs of two sound waves are given in Fig. 10.30. Which wave has (i) greater wavelength, and (ii) smaller amplitude?
(i) Greater wavelength: (a) — it has fewer waves in the same distance.
(ii) Smaller amplitude: (a) — its peaks are lower than those of (b).
6The sound waves emitted by three sources A, B and C are represented in Fig. 10.31. If the frequency of A is maximum and C is minimum, identify the corresponding curves.
Higher frequency means more waves in the same distance (shorter wavelength).
A — Green curveB — Red curveC — Blue curve
7Draw a graph to represent a sound wave for which the density amplitude is 3 units and wavelength is 4 cm.
Density-distance graph. The dashed line is the normal density. Peaks are 3 units above it and troughs 3 units below it. One complete wave repeats every 4 cm.
8In a movie, the explosion of a spacecraft in space is shown with a flash of light and sound at the same time. What are the errors in this depiction?
Space is a vacuum. Sound needs a medium to travel. So no sound of the explosion can be heard in space.
Even where sound can travel (in air), light travels much faster than sound. So the flash would be seen before the sound is heard, not at the same time.
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9A source produces a sound wave of wavelength 3.44 m. If the wave travels at 344 m s−1, find its time period.
f = v/λ = 344/3.44 = 100 Hz
T = 1/f = 1/100 = 0.01 s
10A ship sent a sonar signal and detected an echo after 5 s. If ultrasonic waves travel at 1525 m s−1 in seawater, how far down is the sunken ship?
2d = v × t = 1525 × 5 = 7625 m
d = 7625/2 = 3812.5 m
11A parking sensor emits ultrasonic waves (about 40 kHz). The warning beep starts at 1.2 m from the obstacle. How much time does the wave take to go to the obstacle and come back? (Speed = 345 m s−1)
Total distance = 2 × 1.2 = 2.4 m
t = 2.4/345 ≈ 0.007 s
12The speed of sound in air is about 331 m s−1 at 0 °C and 344 m s−1 at 22 °C. How much extra time will thunder take to travel 1720 m if the temperature changes from 22 °C to 0 °C?
At 22 °C: t1 = 1720/344 = 5 s
At 0 °C: t2 = 1720/331 ≈ 5.196 s
Extra time = t2 − t1 = 65/331 s ≈ 0.2 s
13The variation of density of a medium for a sound wave travelling at 340 m s−1 is shown in Fig. 10.32. Calculate the wavelength and frequency.
The 8 cm length covers two complete waves (two compressions and two rarefactions).
λ = 8/2 = 4 cm = 0.04 m
f = v/λ = 340/0.04 = 8500 Hz
14Two sound waves A and B travel at 345 m s−1 (Fig. 10.33). What is the wavelength of each? Also calculate their frequencies.
From the graph, A completes one wave in 2.5 cm and B in 5.0 cm.
λA = 2.5 cm = 0.025 m ⇒ fA = 345/0.025 = 13800 Hz
λB = 5.0 cm = 0.05 m ⇒ fB = 345/0.05 = 6900 Hz
15Two identical sources are placed at A (in air) and B (in water) (Fig. 10.34). Sound from each goes to the cliff and comes back. If the time taken to return to A is 4.5 times that of B, what is the ratio of the speeds of sound in air and water?
Both sounds travel the same distance. Speed = distance/time, so speed is inversely proportional to time.
