Calculating Properties of a Standing Wave

AI Thread Summary
The wave function for a standing wave on a string is provided, and the discussion involves calculating various properties of the wave. The speed of the wave is calculated to be 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. The original poster expresses uncertainty about the accuracy of their calculations and seeks confirmation. Overall, the calculations appear to be correct based on the provided wave function.
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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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