The wave function y ( x, t ) for a certain standing wave on a string fixed at bo

Question

The wave function y(x, t) for a certain standing wave on a string fixed at both ends is given by
y(x, t) = (0.02 m) sin (2.4 m-1x) cos (490 s-1t). (a) What are the speed and amplitude of the two traveling waves that result in this standing wave?
_____________________          m/s
2_____________________          m

(b) What is the distance between successive nodes on the string?
    ___________________      m

(c) What is the shortest possible length of the string?
4_____________________          m (a) What are the speed and amplitude of the two traveling waves that result in this standing wave?
_____________________          m/s
2_____________________          m

(b) What is the distance between successive nodes on the string?
    ___________________      m

(c) What is the shortest possible length of the string?
4_____________________          m

Explanation / Answer

lambda=2*pi/2.4=2.6167 m

T=2*pi/490=0.0128

==> speed= Lambda/T=2.6167/0.0128=204.43 m/s

==> Amplitude=0.02/2=0.01 m=1 cm

B) the distance between successive nodes on the string=lambda/2=1.308 m

c) shortest length of string =lambda/2=1.308 m

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