How Long Before Hearing a Sonic Boom from a Supersonic Plane at Mach 3?

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SUMMARY

A supersonic plane flying at Mach 3 at an altitude of 20,000 meters produces a sonic boom that reaches a person on the ground directly beneath it. To calculate the time it takes for the sonic boom to be heard, one must use the equation relating speed, time, and distance. The speed of sound is a critical factor in this calculation, and it is assumed to remain constant during the sound's travel from the plane to the observer on the ground.

PREREQUISITES
  • Understanding of Mach number and its implications for speed.
  • Knowledge of the speed of sound in air at standard conditions.
  • Familiarity with basic physics equations relating speed, distance, and time.
  • Ability to apply the concept of sound propagation in different mediums.
NEXT STEPS
  • Research the speed of sound at various altitudes and temperatures.
  • Learn how to apply the formula for speed, time, and distance in practical scenarios.
  • Explore the effects of altitude on sound propagation.
  • Investigate real-world examples of sonic booms and their impact on the environment.
USEFUL FOR

Physics students, aerospace engineers, and anyone interested in the dynamics of sound and supersonic flight will benefit from this discussion.

ScienceGeek24
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Homework Statement



A supersonic plane flies at Mach 3 at an altitude of 20,000 m. A person on the ground sees the plane directly overhead. How much time passes the before she hears the sonic boom?

Homework Equations



f=fo(v+-vo/v-+vs)

The Attempt at a Solution



I don't really know how to start up with this one, I was hoping for some help here.
 
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ScienceGeek24 said:

Homework Statement



A supersonic plane flies at Mach 3 at an altitude of 20,000 m. A person on the ground sees the plane directly overhead. How much time passes the before she hears the sonic boom?

Homework Equations



f=fo(v+-vo/v-+vs)

The Attempt at a Solution



I don't really know how to start up with this one, I was hoping for some help here.

The sonic boom is just a noise produced by the plane, which has to travel 20,000m to reach you.
The answer would be the same if it was a helicopter hovering at 20000m then firing a really loud gun - or with a really big sound system playing AC-DC.
 
So what equation do you suggest I can use to start up the problem?
 
ScienceGeek24 said:
So what equation do you suggest I can use to start up the problem?

You want to calculate the time taken for sound to travel 20000m. What equation do you think you need - it connects speed, time and distance?

You will need to know the speed of sound - and will probably have to make the assumption that it remains constant all the way from up there to down where you are!
 

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