# Physics applied to sound waves -

1.A supersonic jet traveling at Mach 3 at an altitude of 20000m is directly overhead at time t=0.

A) How long will it be before the ground observer encounters the shock wave?

B)Where will the plane be when it is finally heard?(Assume an average value of 330m/s for speed of sound in air)

I will send what I have for this one as attachment.

Just incase you can't see the numbers.. I have the plane 56478m away from the person and at an angle of 19.5degrees and the person hears the sound 181secs after it flies over him.

2.Expectant parents are thrilled to hear their unborn baby's heartbeat, revealed by an ultrasounic motion detector. Suppose the fetus's bentricluar wall moves in simple harmonic motion with amplitude 1.8mm and frequency 115 per minute.

A)Find the maximum linear speed of the heart wall. Suppose the motion detector in contact with the mother's abdomen produces sound at precisely 2 MHz, which travels through tissue at 1.5km/s.

B)Find the maximum frequency at which sound arrives at the wall of the baby's heart.

C)Find the maximum frequency at which reflected sound is received by the motion detector.

(By electronically "listening" for echoes at a frequency different from the broadcast frequency, the motion detector produces beeps of audible sound in synchronization with the fetal heartbeat.)

3.Two ships are moving along a line due east. The trailing vessel has a speed of 64.0km/h relative to a land-based observation point, and the leading ship has a speed of 45.0km/h relative to the same station. The trailing ship transmits a sonar signal at a frequency of 1200Hz. What frequency is monitored by the leading ship? (Use 1520m/s as the speed of sound in ocean water)

The answer is 1204Hz but not sure how to get it... Thanks

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#### Solution Preview

1.

<br>Velocity of shockwave produced at time t=0 at an altitude 20Km is 330 m/s. Thus the time after which it is heard by a person on the ground is 20000/330 = 60.6 Sec

<br>

<br>By this time the plane will have moved a distance 3 x 330 x 60.6 m

<br> = 59994 m

<br>

<br>181 Sec is correct if the plane produced the boom at a distance 59994m away from initial position.

<br>

<br>2.

<br>(a)Ampltude A = 0.0018 m

<br> Frequency f = 115/60 beats/sec = 115/60 Hz

<br>Linear ...

#### Solution Summary

Various applications utilizing the properties of sound as a probe. Easy to understand solutions.

Physics Phenomenon of beating: sound of a siren, beat frequency of two sounds

See attached file for formulas.

Temporal interference results from the superposition of two waves having slightly different frequencies. When the two waves are observed at a point in space, there is a temporal (time) alternation between constructive and destructive interference. If, for example, two tuning forks of slightly different frequencies are struck, one hears a sound of periodically varying amplitude. This phenomenon is called beating, and the number of amplitude maxima one hears per second gives the beat frequency. (a) Let the time-dependent variations of the displacement due to two sound waves of slightly different frequencies, at a point where kx = π /2, be

and

where ω1 > ω2. Use the principle of superposition to show that the resulting displacement is

where and . (b) The derivation in (a) shows that the resultant displacement is a cosine function whose angular frequency is ω and whose time varying amplitude is the absolute value of the quantity in the brackets. Show that the number of beats per second (periodically varying amplitude) is . (c) A siren emitting a sound of 1000 Hz moves away from you towards the face of a cliff at a speed of 10 m / s. Take the speed of sound in air as 330 m / s. You hear the direct sound of the siren and the sound reflected from the cliff. What is the beat frequency of these two sounds? Is it perceptible (it must be less than 20 Hz to be perceived)?

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