Calculating Properties of a Standing Wave

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SUMMARY

The wave function for a standing wave on a string fixed at both ends is represented as y(x, t) = (5.00 cm) sin (2.50 m^(−1)x) cos (500 s^(−1)t). The calculated speed of the wave is 200 m/s, with an amplitude of 5.0 cm. The distance between successive nodes is determined to be 1.26 m, which also represents the shortest possible length of the string. These calculations are confirmed as correct based on the provided wave function parameters.

PREREQUISITES
  • Understanding of wave functions and their components
  • Knowledge of standing waves and their properties
  • Familiarity with the concept of nodes and antinodes
  • Basic skills in trigonometry and unit conversions
NEXT STEPS
  • Study the principles of wave superposition in physics
  • Learn about the properties of standing waves in fixed boundary conditions
  • Explore the relationship between wave speed, frequency, and wavelength
  • Investigate the mathematical derivation of wave functions
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Students studying physics, particularly those focusing on wave mechanics, as well as educators seeking to enhance their understanding of standing waves and their properties.

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Homework Statement



The wave function for a certain standing wave on a string that is fixed at both ends is given by
y(x, t) = (5.00 cm) sin (2.50 m^(− 1)x) cos (500 s^(− 1)t)


A standing wave can be considered as the superposition of two traveling waves.

1.
a. Give the speed in m/s rounded to a whole number.
b. Give the amplitude in cm rounded to one decimal place



2. What is the distance between successive nodes on the string? Give your answer in m rounded to two decimal places.


3. What is the shortest possible length of the string? Give your answer in m rounded to two decimal places.


Homework Equations





The Attempt at a Solution



I got all the answers:

1a. 200m/s
1b. 5.0 cm
2. 1.26 m
3. 1.26 m

But I am sure about none of them, please check if right or not? If it's not, then please help me out. Thanks !
 
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