Finding wavelength from counting crest

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SUMMARY

The discussion focuses on calculating the distance a wave group extends on the surface of water after a stone is tossed into it, with a wave speed of 25 cm/s and a disturbance duration of 4.0 seconds. The group distance is determined by multiplying the wave speed by the time, resulting in a distance of 100 cm. Additionally, the observer counts 12 wave crests, leading to the calculation of the wavelength as 100 cm divided by 12, which is approximately 8.33 cm. The conversation emphasizes the distinction between counting crests and wavelengths, highlighting the importance of accurately interpreting wave characteristics.

PREREQUISITES
  • Understanding of wave mechanics and properties
  • Familiarity with the concept of wave speed and wavelength
  • Knowledge of the classical uncertainty relationship in physics
  • Basic mathematical skills for calculations involving distance and time
NEXT STEPS
  • Study the principles of wave propagation and wave speed calculations
  • Learn about the classical uncertainty principle and its applications in wave physics
  • Explore the relationship between wave crests and wavelengths in various waveforms
  • Investigate practical examples of wave behavior in different mediums, such as water and sound
USEFUL FOR

Students studying physics, particularly those focusing on wave mechanics, as well as educators and anyone interested in understanding the relationship between wave characteristics and measurements.

aryan
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Homework Statement

[/B]
A stone tossed into a body of water creates a disturbance at the point of impact that lasts for Dt = 4.0s. Measurements indicates that the wave speed is v = 25 cm/s. (a) Over what distance on the surface of water does the wave group extend? (b) An observer counts 12 wave crests in the group.Use the classical uncertainty relationship to estimate the precision with which the wavelength could be determined.

Homework Equations


delta(x) * delta (k) >= PI[/B]

The Attempt at a Solution


the group distance is calculated by multiplying wave speed*the time impact (b) there are 12 crest over the distance of 100 cm hence the wavelength will be 100/12. I am not sure about this is there any mistake in this?[/B]
 
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Welcome to PF;
The only thing I can think of is that 12 crests is not always the same as 12 wavelengths ... sketch a wave with 12 crests and count the wavelengths.
 

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