(III) A source emits sound of wavelengths 2.54 m and 2.72 m in air. (a) How many

Question

(III) A source emits sound of wavelengths 2.54 m and 2.72 m in air. (a) How many beats per second will be heard? (Assume T = 20 degree C) (b) How far apart in space are the regions of maximum intensity? (I) The predominant frequency of a certain fire truck's siren is 1650 Hz when at rest. What frequency do you detect if you move with a speed of 30.0m/s (a) toward the fire truck, and (b) away from it? (II) A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 27.5 m/s. What is the received sound frequency? (II) Two automobiles are equipped with the same single- frequency horn. When one is at rest and the other is moving toward the first at 18 m/s, the driver at rest bears a beat frequency of 4.5Hz. What is the frequency the horns emit? Assume T = 20 degree C. (II) As a bat flies toward a wall at a speed of 6.0 m/s, the bat emits an ultrasonic sound wave with frequency 30.0kHz. What frequency does the bat hear in the reflected wave? (II) In one of the original Doppler experiments, a tuba was played at a frequency of 75 Hz on a moving flat train car, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard in the station if the train car approached the station at a speed of 14.0 m/s? (II) A wave on the ocean surface with wavelength 44 m travels east at a speed of 18m/s relative to the ocean floor. If, on this stretch of ocean, a powerboat is moving at 14 m/s (relative to the ocean floor), how often does the boat encounter a wave crest, if the boat is traveling (a) west, and (b) east?

Explanation / Answer

55)

(a)

At 20° the speed of sound is

c = 343m/s

The frequencies of the two waves are

f = c/ = 343m/s / 2.54m = 135 s¹

f = c/ = 343m/s / 2.72m = 126 s¹

The beat frequency is the absolute value of the frequency difference:

f_beat = | f - f | = | 135 s¹ - 126 s¹ | = 9 s¹

That means you hear about 9 beats per second.

(b)

_beat = c / f_beat = 343m/s / 9 s¹ = 41.44 m

The regions of maximum intensity are about 41.44 m apart.

56)

Actual frequency of sirun = n =1650 Hz

apparent frequency

n' = n [v - vo] / [v - vs]

in this combined formula, all v, vo, vs are moving in one direction (say +x). if 1 is in opposite direction, then it has to

be resoved in +x.

v = speed of sound = 343 m/s

a)

let source (engine) at origin. vs = 0 given

vo = - 30 m/s (observer going to source, -ve x, so made in +x direction)

v = + 343 m/s sound speed moving in + x (reaching observer)

n ' = 1650 [343 - (-30)] / [343- 0]

n ' = 1650*[1.087] = 1793.55 Hz

b)

away from engine

v = +343 , vo = + 30 , vs =0

n ' = 1650 [343 - 30] / [343 - 0]

n ' = 1650*[0.9125] = 1505.625 Hz

57)

f = f0*(c-vr)/(c+vr)

c = 343 m/s

f0 = 50 x 10^3

vr = 27.5 m/s

f = (50 x 10^3)*[(343 - 27.5) / (343 + 27.5)

f = 42.57 kHz

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