Phys 1L03 Tutorial session Set 10
Tenth series: Wave, sound wave
1. At Zion National Park a loud shout produces an echo 1.85 s later from a colourful sandstone cliff.
How far away is the cliff?
2. Four waves are described by the following equations, all distances measured in centimeters and all
time in seconds
ya =10cos(3 x− 4 )
y =10cos(5 +4 ) t
b
yc = 20cos(−10 +60 ) t
y = 20cos(−4 −20 ) t
d
a. Which waves travel in the +x-direction?
b. Which waves travel in the –x-direction?
c. Which wave has the highest frequency?
d. Which wave has the greatest wavelength?
e. Which wave has the greatest speed?
3. The three waves, A, B, C shown propagate on strings with equal tensions and equal mass per length,
hence having the same speed. Rank the waves in order of increasing:
a. frequency,
b. wavelength
4. In Fig Below, Pipe A is made to oscillate in its third harmonic by a small internal sound source.
Sound emitted at the right end happens to resonate four nearby pipes, each at with only one open end
( they are not drawn to scale). Pipe B oscillates in its lowest harmonic, pipe C in its second lowest
harmonic, pipe D in its third lowest harmonic, and pipe E in its fourth lowest harmonic. Without
computation, rank all five pipes according to their length, greatest first. (Hint: Draw the standing
waves to scale and then draw the pipes to scale).
5. The displacement of the wave traveling in + x direction is: Y(x, t) = 0.35 (m) Sin (6x- 30t); where x
is in meter and t is in second.
a. If the wave reaches its maximum displacement after 0.04 sec, what is the value of x
corresponding to y (max).
b. How long does it take for the wave to take the total distance of 4 cycles?
Solution:
1 6. At a distance of 30m from a jet engine, the sound intensity level is 130 dB. Serious, permanent
hearing damage occurs rapidly at intensity levels this high, which is why you see airport personnel
using hearing protection out in the runway. Assume the engine is isotropic and ignore reflections and
absorption. At what distance is the intensity level 110 dB – still quite loud but below the threshold of
I I L10
pain? IL = 10 log I = (10 )I 0
I0
7. The song of the Brown Creeper is very high in frequency – as high as 8 kHz. Many people who
have lost some of their hearing can’t hear it at all. Suppose that you are out in the woods and hear the
song. If the intensity of the song at your position is 1.4x 10 – 8W/m , and the frequency is 6.0 kHz,
what are the pressure and displacement amplitudes? (Assume the temperature is 20 degrees Celsius.)
P0 ⇒ P =0 2I ρv v = 343 m/s P 0 ω vρ A 0
I = 2ρ v

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